| PS25P | Ag4 | m | (John, age 50, teacher) unspecified |
| PS25R | Ag1 | m | (Ian, age 16, student) unspecified |
| FY9PSUNK (respondent W0000) | X | u | (Unknown speaker, age unknown) other |
| FY9PSUGP (respondent W000M) | X | u | (Group of unknown speakers, age unknown) other |
| Unknown speaker (FY9PSUNK) | [...] |
| John (PS25P) |
[1] So direct proportionality. |
| Ian (PS25R) |
[2] And inverse. |
| John (PS25P) |
[3] Not too too much trouble with that. [4] Okay if erm so [...] one of the questions that comes up a lot is speed and distance and time. [5] And that's a good example of both types [...] there. [6] So let's say we keep the erm You've got to get from here to Birmingham. [7] If you go faster, erm what happens to the time it takes? |
| Ian (PS25R) |
[8] Less time. |
| John (PS25P) |
[9] Right. [10] So if I go twice as fast, does that mean it's gonna take me twice as long to get there? |
| Ian (PS25R) |
[11] No. |
| John (PS25P) |
[12] No. [13] So it's inversely proportional . |
| Ian (PS25R) |
[14] Yeah. |
| John (PS25P) |
[15] If I go twice as fast, it'll take me one over two, so that's a half as long. [16] Okay right. [17] If I go ten times as fast, I get there in one tenth of the time. [18] And that's all it is. [19] That's all the inverse proportionality. [20] Direct proportionality, if I'm driving at a steady sixty miles an hour, how far would I go in erm one hour? [21] Sixty miles. [22] How far would I go in ten hours, if I'm going at a steady sixty miles an hour? [23] How far would I go? [24] Doing sixty miles every hour, and I keep going for ten hours. [25] So |
| Ian (PS25R) |
[26] Six hundred, |
| John (PS25P) |
[27] So so I do six hundred miles. [28] Erm If I've got sixty miles to do, and I do it at erm do it at sixty miles an hour, it takes me one hour. [29] If I do it at half the speed, just do it at thirty miles an hour, how long will that take? |
| Ian (PS25R) |
[30] Two hours. |
| John (PS25P) |
[31] If I do it at half the speed. [32] Trying to cover a a distance. [33] Trying to cover sixty miles, okay, Trying to cover sixty miles so I do it again at sixty miles an hour. [34] Takes one hour. [35] Now if I do it at half that speed, if I do if I drive at thirty miles an hour, how long will it take me to do the sixty miles? |
| Ian (PS25R) |
[36] Two hours. |
| John (PS25P) |
[37] Right. [38] Two hours. [39] So this is the speed and distance and time thing gets very confusing, because some of it is direct proportional, right so the faster you go, the more distance you could travel in a fixed in an hour say. [40] Obviously sixty miles an hours means if you keep going for an hour, you do sixty miles. [41] Thirty miles an hour, keep going for an hour you'll only do thirty. [42] So how far you go is directly proportional to how fast. |
| Ian (PS25R) |
[43] Yeah. |
| John (PS25P) |
[44] If you say, How far would you go in an hour, keep the time fixed so we're not changing all three things, cos then it's really confusing. [45] So keep one of them fixed. [46] Change another one. [47] So it's keep the first one fixed, change the second one, and see how the third one changes. [48] And most of it If you try and do it with sort of the squiggles on the paper. [49] [...] equations [...] this one go on the top or the bottom of the fraction or what? [50] But if you just back off [...] bit. [51] And you think, Well hang on let's just do it a bit of common sense. [52] And apply it to say driving along at steady speeds, then you can work a lot of it out for yourself. [53] And erm you'll get should get happier with that. [54] So let's try a few examples. [55] Erm for you to do. [56] When I say let's try, I mean you can try some. [57] So if we've got let's say sixty miles an hour. [58] A fixed speed of sixty miles an hour. [59] And we want to travel a hundred a hundred and twenty miles. [60] How long will that take? |
| Ian (PS25R) |
[61] Two hours. |
| John (PS25P) |
[62] That will take two hours. [63] And suppose I go twice as fast. [64] Right double the speed, if I drive at a hundred and twenty. [65] Now how long w will it take me. |
| Ian (PS25R) |
[66] One hour. |
| John (PS25P) |
[67] That's only half the time it took me last time. [68] So that's a half of two, which is one hour. [69] Okay so here. [70] Twice the speed. [71] Erm what would happen if I drive at a tenth of the speed? [72] One tenth of the speed. [73] ... I drive at six miles an hour. [74] Hey? ... it's the original time, which was two hours, is times it's times a tenth. [75] No |
| Ian (PS25R) | [...] |
| John (PS25P) |
[76] No is that right? [77] What's going on here? [78] If I drive at a tenth of the speed, is it gonna take me longer or is it gonna take me is it gonna be quicker? |
| Ian (PS25R) |
[79] Longer. |
| John (PS25P) |
[80] It's gonna be longer, so it can't be a tenth of it. |
| Ian (PS25R) |
[81] No. |
| John (PS25P) |
[82] Right, here we went at twice the speed, and it finished up half the time. [83] Now we're driving a tenth of the speed, so it's going to be one over one tenth. [84] Which is ten times. [85] So it would take me twenty hours of I drive at six miles an hour. |
| Ian (PS25R) |
[86] Yeah, |
| John (PS25P) |
[87] Right. [88] And that ties up When you get it like this [...] a tenth of the speed. [89] What we've got now is, it's directly proportional, but they've got a fraction in. [90] [laugh] So it's making it look like inverse proportion and the first thought is, Oh it l er er oh. [91] Well it'll take a tenth of the time wouldn't it. [92] No it takes ten times as much. [93] [...] half the speed, it'll take you twice as long. [94] Erm that's thinking of a steady speed. [95] That's a fixed speed. [96] I'm just sort of rushing through this a bit, and I'm trying to show where the where most people get it wrong. [97] Erm and so you can watch out for those the traps. [98] Now if it's a fixed distance, fixed distance, let's say we're going to go, a hundred and twenty miles. [99] Right, and we're not gonna change the distance now, we're keeping that fixed. [100] If we drive at ... sixty miles an hour. [101] Erm we've done the time there. [102] Right. [103] Er ... Right. [104] What are we do Hang on, let's just check what we're doing with this. [105] Fix First one we did was fixed speed, sixty miles an hour, we go double the speed, so what happens to the time? [106] Er that should have been a fixed a fixed distance there [...] . [107] Fixed distance. [108] ... A fixed distance er sixty miles say. [109] Er say a fixed distance of a hundred and twenty miles. [110] That's more like it. [111] Okay. [112] And it we drive it at sixty miles an hour, for two hours. [113] Now if we keep the distance er let's see that was the fixed distance. [114] If we keep the speed fixed now we have Do the one I should have done first. [115] Fixed speed of sixty miles an hour. [116] Okay. [117] ... And we'll try How long would we go in how far in one hour? |
| Ian (PS25R) |
[118] Sixty miles. |
| John (PS25P) |
[119] Right. [120] Okay. [121] How far in erm ... three and a half hours? ... |
| Ian (PS25R) |
[122] A hundred and fifty miles an |
| John (PS25P) |
[123] That was very good. [124] That was brilliant yeah. [125] Yeah exactly. [126] How did you work that out? |
| Ian (PS25R) |
[127] Well it's double that hang on |
| Unknown speaker (FY9PSUNK) | [whispering] [...] [] |
| John (PS25P) |
[128] it's close. |
| Ian (PS25R) |
[129] Mm. |
| John (PS25P) |
[130] How far would we go in three hours? |
| Ian (PS25R) | [...] |
| John (PS25P) |
[131] At a steady sixty miles an hour. [132] How far would we go ? |
| Ian (PS25R) |
[133] A hundred and eighty. |
| John (PS25P) |
[134] Right. [135] So we'll go a hundred and eighty in the first three hours. [136] And how long would we go in the last half hour? [...] |
| Ian (PS25R) |
[137] Thirty. |
| John (PS25P) |
[138] And we'd do another thirty miles. |
| Ian (PS25R) |
[139] Yeah. |
| John (PS25P) |
[140] Okay. [141] So two hundred and |
| Ian (PS25R) |
[142] Two hundred and ten. |
| John (PS25P) |
[143] Two hundred and ten miles we do. [144] Now you can do that straight off. [145] Instead of doing it a bit at a time, we can just multiply it. [146] And say three and a half times sixty. [147] Just do it that way which is what you'd normally do, on your calculator, you'd just do sixty times three point five. [148] Now that's that's a very quick look. [149] Erm don't worry if you don't understand it all. [150] Now hove you got the problem that you had? |
| Ian (PS25R) |
[151] Yeah I've got it here. [...] |
| John (PS25P) |
[152] Well look through that and I wa what I want now is if you, can try and work your way through it. [153] Without Okay. |
| Ian (PS25R) |
[154] [laughing] Go on. [155] [laugh] You haven't seen it yet. [] |
| John (PS25P) |
[156] Well er if it's a messy one, the first thing to do with it, is to split it up into little bits. [157] I noticed [...] . |
| Ian (PS25R) |
[158] This one. [159] A and B are okay. [160] I can get that. |
| John (PS25P) |
[161] Ah. |
| Ian (PS25R) |
[162] It's C and D. |
| John (PS25P) |
[163] Right. [164] [reading] Six swallows ate three hundred flies in five hours. [165] Complete the following. [166] ... Six swallows eat sixty flies in how many hours? [167] Right. [168] And how many swallows would eat six thousand flies in five hours? [] [169] Right erm ... Okay talk about it. [170] You said A and B were okay. [171] How did you do A? |
| Ian (PS25R) |
[172] Yeah. [173] Well you had six eating three hundred, so yo I divided three hundred by six. [174] And timesed it by thirty. [175] And that gave me how many flies were gonna be eaten. |
| John (PS25P) |
[176] Okay and why why did you divide it that way round? |
| Ian (PS25R) |
[177] Cos the number of flies into swallows. |
| John (PS25P) |
[178] Okay. [179] So this is a bit like the speed and the distance and the time and things isn't it. [180] All combined . |
| Ian (PS25R) |
[181] Yeah. |
| John (PS25P) |
[182] Erm ... so we need really equations for all of these. [183] Cos they're like if you like. [184] So let's have a look at it could you could you find out from the the question here, six swallows ate three hundred flies in five hours. [185] Can you find out how many flies, one swallow would eat in one hour? [186] ... Or could you find out how many flies one swallow would eat in five hours? |
| Ian (PS25R) |
[187] Yeah. |
| John (PS25P) |
[188] Yeah? [189] How would you do that? [190] So we've got six swallows eat three hundred flies in five hours. [191] Okay. [192] How many would one eat in five hours? [193] ... Okay? |
| Ian (PS25R) |
[194] Fifty. |
| John (PS25P) |
[195] Right. [196] So one swallow would eat fifty in five hours. [197] How much would one swallow eat in one hour then? |
| Ian (PS25R) |
[198] Ten. |
| John (PS25P) |
[199] Okay so you you you've got it now, that one swallow eats one fly erm sorry eats ten flies |
| Ian (PS25R) |
[200] Ten flies in one hour. |
| John (PS25P) |
[201] In an hour. |
| Ian (PS25R) |
[202] I'll write that down. |
| John (PS25P) |
[203] Okay so write that and then we'll check it. [204] ... Right. [205] Now let's check it. [206] Let's see if it gets back to what they said there. [207] Six swallows erm would they How many would six swallows eat in one hour? |
| Ian (PS25R) |
[208] Sixty. |
| John (PS25P) |
[209] Okay. [210] So we that'll just we multiply that by six. [211] or how much six swallows would eat. [212] And you get sixty. [213] Right and how much would they so if they if these six swallows are eating sixty |
| Ian (PS25R) |
[214] Three hundred. |
| John (PS25P) |
[215] in one hour. |
| Ian (PS25R) |
[216] Erm. |
| John (PS25P) |
[217] [...] That's it. |
| Ian (PS25R) |
[218] Er in five hours. |
| John (PS25P) |
[219] Right so ... if we're looking at what what are they they asking for here? [220] How long will they take and how many swallows, and on this one how many flies. [221] Right. [222] ... So which which ones are proportional to what? [223] If you've got more swallows, do more flies get eaten? |
| Ian (PS25R) |
[224] Yeah. |
| John (PS25P) |
[225] And if you've got more time, for them to eat, do more flies get eaten? |
| Ian (PS25R) |
[226] Yeah. |
| John (PS25P) |
[227] So they're both directly proportional. [228] Okay. [229] Now just talk about C. [230] Now that you've worked out how many one swallow eats in one hour. |
| Ian (PS25R) |
[231] [whispering] Swallows. [] [232] ... Er |
| John (PS25P) |
[233] How many would they eat in How many would six swallows east in one hour? |
| Ian (PS25R) |
[234] Sixty. |
| John (PS25P) |
[235] Okay. [236] It says here six swallows eat sixty flies in |
| Ian (PS25R) |
[237] Six hours. |
| John (PS25P) |
[238] how many hours? |
| Ian (PS25R) |
[239] Six hours. |
| John (PS25P) |
[240] Well we've got here, we've got one swallow eats ten flies in one hour. [241] Okay. [242] We have six times as many swallows, if we have six swallows. [243] Just write down how many six swallows will eat in one hour. [244] So just write it as six times ten or ten times six. [245] Okay. [246] Are you happy with that? |
| Ian (PS25R) |
[247] Yeah. |
| John (PS25P) |
[248] One of them will eat ten flies every hour, so if we got six of them it'll be ten times six. [249] In one hour. [250] And that comes to sixty, and the question here is six swallows eat sixty flies in how many hours? [251] So what's the answer to that one? |
| Ian (PS25R) |
[252] One hour. |
| John (PS25P) |
[253] Just one hour. [254] Okay. [255] So you've done C. |
| Ian (PS25R) |
[256] Yeah. |
| John (PS25P) |
[257] Now D. [258] How many swallows would eat six thousand flies in five hours? [259] Well six of them eat three hundred right. [260] If they going to get through six thousand, are you going to need more swallows or less swallows? |
| Ian (PS25R) |
[261] More swallows. |
| John (PS25P) |
[262] Okay. [263] So have a guess at what you multiply or divide by there. [264] Just to, not sort of working out just what what you see it it probably is. |
| Ian (PS25R) |
[265] Six thousand divide by three hundred. |
| John (PS25P) |
[266] That's it. [267] Six thousand divided by three hundred. [268] Erm and what about the six, that's where that comes in and starts confusing things isn't it? |
| Ian (PS25R) |
[269] Yeah. |
| John (PS25P) |
[270] So if you just did, six thousand divided by three hundred. [271] It wouldn't tell you how many swallows, it would tell you how many lots of six swallows would east that. |
| Ian (PS25R) |
[272] Then you multiply it by six. |
| John (PS25P) |
[273] Then you have to you've got what your your answer Let let's say, we keep our swallows in cages. [274] Right six swallows in each cage. [275] And we sort of go and feed them three hundred flies, every five hours. [276] And then somebody comes along and says, Oh we've got a some big order on, we're got to feed them six thousand flies, in five hours. [277] So you first thing you says, Well how many cages are there then? [278] One cage one cage of swallows get through three hundred in five hours, so six thousand divided by three hundred. [279] That would be the number of cages of |
| Ian (PS25R) |
[280] Cages. |
| John (PS25P) |
[281] swallows. [282] That |
| Ian (PS25R) |
[283] Yeah. |
| John (PS25P) |
[284] you'd need to get through the six thousand flies. [285] And then you say, Now how many how many swallows in a cage? [286] And you said multiply by didn't you. |
| Ian (PS25R) |
[287] Yeah. |
| John (PS25P) |
[288] Sorry that's right. [289] Yeah, multiply by. [290] So ... six thousand ... Yeah it's alright [...] problem. [291] Six thousand by ... divided by ... |
| Ian (PS25R) |
[292] Three. |
| John (PS25P) |
[293] three hundred, tells you how many cages you need. [294] And there's six swallows in every cage, so when you get that answer, you just multiply it by six. [295] So you want to work that one out? [296] What that'll come to? [297] And er just sort of work it out on here cos a lot'll cancel. [298] ... We'll start from, six swallows eat three hundred. [299] Yeah. [300] Are you are you are you happy with this, or am I confusing you. [301] I think I'm confusing |
| Ian (PS25R) |
[302] Yeah. |
| John (PS25P) |
[303] you actually. |
| Ian (PS25R) |
[304] No I get I get ... the idea there. |
| John (PS25P) |
[305] Yeah. |
| Ian (PS25R) |
[306] [whispering] Six thousand divide by that. [] [307] Yeah I get that. |
| John (PS25P) |
[308] Mm. |
| Ian (PS25R) |
[309] That. [310] I don't know what you mean by cancelling down though. |
| John (PS25P) |
[311] Ah. |
| Ian (PS25R) |
[312] You know I I I've cancelled down before but you know in this like. [313] In |
| John (PS25P) |
[314] Right. |
| Ian (PS25R) |
[315] [...] down like this. [316] Never cancelled d I've cancelled down like equations and things . |
| John (PS25P) |
[317] Right If you're cancelling down [...] . [318] You were doing erm six thousand divided by three hundred, that tells you how many cages and there's six swallows in every cage, times six. [319] Okay. [320] Now this was flies that the old ones ate flies the new ones ate. [321] There's going to be eating more flies, so you need more swallows, so that looks the right way up. [322] And we weren't thinking about how many one ate, we were thinking about how many six ate. [323] So it'll take more of them. [324] So we can cancel that. [325] Divide three by a hundred. [326] Sorry divide three hundred by a hundred. [327] What do we get? |
| Ian (PS25R) |
[328] Three. |
| John (PS25P) |
[329] And divide this by a hundred, what do we get? |
| Ian (PS25R) |
[330] Sixty. |
| John (PS25P) |
[331] Okay and then divide that by three? |
| Ian (PS25R) |
[332] One. |
| John (PS25P) |
[333] And that by three. |
| Ian (PS25R) |
[334] Three. [335] [laughing] No no. [] |
| John (PS25P) |
[336] How many threes in six? |
| Ian (PS25R) |
[337] Two. |
| John (PS25P) |
[338] Okay. [339] ... So it just comes to? |
| Ian (PS25R) |
[340] A hundred and twenty. |
| John (PS25P) |
[341] A hundred and twenty. [342] Erm don't bother about that about the cancelling. [343] Erm, no. [344] Do it do it on your calculator, just put the figures in and do it. [345] But then think about it when you got your answer, if it seems okay. [346] [cough] Er ... this is this is the one that you get a lot. [347] About cars doing journeys. [348] And this is the other big one that you get about erm ... food. [349] That's the other one too. [350] Four men do a job in twelve hours. [351] How many men would it take to do the job in two hours? [352] ... Right. [353] ... This sort of thing. [354] [reading] Twelve men build a wall in eight hours. [355] How long would it take four men to do it? [] [356] So let's just talk about that without doing erm a particular ... example. [357] Er ... Twelve men ... take So they're building a wall or something. [358] Twelve men take eight hours. [359] Okay? [360] Erm how many men would we need if we wanted it built in four hours. [361] Just to just to guess at it without sort of working it out. [362] What would you say? ... |
| Ian (PS25R) |
[363] S Twenty four men. |
| John (PS25P) |
[364] Right. [365] If you want it done in half the time, you've got to have twice as many people. |
| Ian (PS25R) |
[366] Yeah. |
| John (PS25P) |
[367] Yeah. [368] Erm ... that's inverse proportion, that's the hard one, and I think you understand what you're doing. |
| Ian (PS25R) |
[369] Yeah. |
| John (PS25P) |
[370] Very well actually in there. [371] Erm ... you'll see a lot of them like this. [372] Four men. [373] Try try nine. [374] Completely on your own then. [375] Four men do a job in twelve hours. [376] How many to do the job in two hours? ... |
| Ian (PS25R) |
[377] Forty eight men? |
| John (PS25P) |
[378] Now how did you work it out? |
| Ian (PS25R) |
[379] Well it takes fo four men, twelve hours to do the job. [380] So in two hours, you've got to have ... twelve times as many men as you've already got. |
| John (PS25P) |
[381] Oh. [382] where do you get your twelve from? |
| Ian (PS25R) |
[383] Here. |
| John (PS25P) |
[384] Let's let's make it a slightly different problem. [385] Lets' say, erm four men take twelve hours. [386] Okay. [387] How many men would you need to do the job in six hours? |
| Ian (PS25R) |
[388] Eight men. |
| John (PS25P) |
[389] Right. [390] You only spend half the time, you have twice as many men. [391] How long how many how many men would you need if you want it done in a quarter of the time? [392] If you wanted it done in three hours? ... |
| Ian (PS25R) |
[393] Twelve men. [394] [whispering] Twelve men. [] ... |
| John (PS25P) |
[395] Let's let's forget about the numbers. [396] Let's say we don't know how many men there's erm just one gang of men. [397] So we dunno how many men in a gang. [398] And it takes them twelve hours to do this job. [399] And the foreman comes up and says, Oh want this job in half the time. [400] So [...] we need two gangs to do it. [401] If he comes up and he says, Well we want this job done in a quarter of the time. |
| Ian (PS25R) |
[402] Four times. |
| John (PS25P) |
[403] Four times as many. [404] He says, We want this job done in a tenth of the time. |
| Ian (PS25R) |
[405] Ten times. [406] Yeah. |
| John (PS25P) |
[407] Ten times as many. [408] If he says, Oh well, this isn't a rush job, we want this job to take twice as long as usual. |
| Ian (PS25R) |
[409] Shorten the half the |
| John (PS25P) |
[410] That's it. [411] Just have half the number of men working on it and then it'll take twice as long. [412] Okay. [413] Now in this case, four of them will take twelve hours. [414] Let's say four men is one gang. [415] So forget about you know, like think of a cage of swallows. [416] That's one gang. [417] So one gang of men take twelve hours. [418] What we want is only two hours. [419] So how many gangs are we going to need. [420] ... Are we going to need more men or less more gangs or less gangs? [421] To get it done in |
| Ian (PS25R) |
[422] More gangs. |
| John (PS25P) |
[423] We're going to do more. [424] Going to need more. [425] So we want to do this is in a sixth of the time, right? [426] We want it done ... two twelfths of the time. [427] That's how many gangs erm that's two twelfths of the time, so it's one sixth. [428] This is one sixth of the time. [429] Now we want this job in one sixth of the time. [430] That is takes on gang to do. ... |
| Ian (PS25R) |
[431] Six more gangs. |
| John (PS25P) |
[432] So we'll need six gangs all together. [433] [whispering] Okay? [] [434] Cos that comes to one sixth. [435] We need six gangs. [436] One sixth of the time. [437] So six gangs. [438] Okay. [439] And then you can think of I mean this is this is just sort it can be there to confuse you while you're sorting out the time. [440] And when you're sorted it out, they want six gangs, so that's six times four. [441] So we need ... twenty four men |
| Ian (PS25R) |
[442] Twent |
| John (PS25P) |
[443] on that one. [444] [...] there's four men in in that gang. [445] Now going back to it. [446] So that was four men do it in twelve hours, how many in two. [447] Erm let's see if [...] . [448] Oh that's that's nasty that, because they've got six in both of them. [449] Six women do a job in eight hours. [450] How many women will it take to do the job in six hours? ... |
| Ian (PS25R) |
[451] [whispering] Two. [] ... |
| John (PS25P) |
[452] Think about that one. [453] Are you going to need more, more women or less women? |
| Ian (PS25R) |
[454] More women. |
| John (PS25P) |
[455] Gonna need more. [456] So which way up is the fraction going to go? [457] The first thing to do is forget about the six for a minute. [458] Right It's not six women, it's one gang. [459] ... Right one gang take eight hours. [460] ... So how many gangs are you going to need, to get this job done in six hours? ... |
| Ian (PS25R) |
[461] Well two gangs are gonna get it done in four hours. |
| John (PS25P) |
[462] Right two gangs in four hours, so we don't need two whole gangs. |
| Ian (PS25R) |
[463] Yeah. |
| John (PS25P) |
[464] So that'd be too many. [465] So one gang takes eight hours. [466] How many gangs would take six hours? [467] This is where it's the inverse proportion. [468] It's going to take eight over six. [469] ... Right? [470] Eight over six which comes to? |
| Ian (PS25R) | [...] |
| John (PS25P) |
[471] One and one and a bit gangs. [472] That seems to that looks sensible it seems to [...] . [473] So it's eight over six gangs. [474] ... And how many in a gang? |
| Ian (PS25R) |
[475] Six. |
| John (PS25P) |
[476] Six. [477] So the number of women that we'll want, is eight over six, times six. [478] That'll just cancel that. [479] And we finish up with eight women. [480] Well that's interesting, because six women do the job in eight hours, and it would take eight women to do it in six hours. [481] ... [...] So if we had something like [...] that page [...] . [482] Have you ever heard of the term, man hours? |
| Ian (PS25R) |
[483] Yeah. |
| John (PS25P) |
[484] It takes so many man hours. [485] Erm like to ... decorate a house well no let's say in in a factory, there's erm they've a rush order, they want to get some stuff out and they're going to need another hundred and twenty man hours. [486] to get this job done. [487] Now man hours, is just men times hours. [488] And if you look at this, I mean this is actually women hours, but if you look at that. [489] See what happened with this one that we worked out. [490] Four men do the job in twelve hours. [491] How many man hours do we need altogether? [492] How many man hours does this job take? ... |
| Ian (PS25R) |
[493] Four times twelve. |
| John (PS25P) |
[494] That's it four times twelve. [495] So number nine, the job takes, four men times twelve hours equals four times twelve man hours. [496] Okay. [497] Now if I wanted this job done in six hours, how many men would I need? |
| Ian (PS25R) |
[498] Er |
| John (PS25P) |
[499] Four men take twelve hours. [500] I want the job done in six hours. |
| Ian (PS25R) |
[501] Eight men. |
| John (PS25P) |
[502] I'd make I'd take eight, be twice as much. [503] Now if I said, how long would three men take to do it? [504] It's a bit awkward isn't it. |
| Ian (PS25R) |
[505] Yeah. |
| John (PS25P) |
[506] But one way of looking at it is, Well the job takes forty eight man hours. [507] Forty eight man hours. [508] So how long, how many hours would three men have to work, before they'd made up forty eight man hours? |
| Ian (PS25R) |
[509] Forty eight divided by three. |
| John (PS25P) |
[510] Right. [511] So three men times X if you like, X hours, equals forty eight man hours. [512] And you can all of these, all of the ones where they say, so many men or women take so long to do a job, how many. [513] You can do them all, just be looking at that. [514] You see multiply what they give you. [515] Right. [516] The men times the hours. [517] And that's fixed. [518] That's how many man hours, that job takes. [519] And then if they say, Well so three men would take forty eight divided by three hours. [520] Yeah? |
| Ian (PS25R) |
[521] Yeah. |
| John (PS25P) |
[522] Okay e divided each side by three, X equals forty eight over three. [523] Erm ... It takes forty eight man hours. [524] If I said, I want this job done in two hours. [525] How would you work it out? [526] The job takes forty eight man hours, and I want it done in two hours. [527] So how many men would we need? |
| Ian (PS25R) |
[528] Forty eight hours. [529] Well that's three men. ... |
| John (PS25P) |
[530] Yes when when there were three men Right when there were three men, that's how many hours it took. [531] Now a different problem, erm it still takes forty eight man hours, but this time how many men to do the job in two hours? [532] ... Is it going to take more men or less men to get this job done? |
| Ian (PS25R) |
[533] More men. |
| John (PS25P) |
[534] Mm. [535] So you can work it that way, you can think of that as a check. [536] But the easy way, as I say, is to just concentrate on the man hours. [537] This job, whatever it is, it takes forty eight man hours. [537_1] So if you multiply the number of men, by the h number of hours they work, it's going to always come to forty eight. [538] So if you'd like er we don't know how many men. [539] Let's say it's X. [540] X times two hours has got to be equal to |
| Ian (PS25R) |
[541] Forty man hours. |
| John (PS25P) |
[542] Right that's got to be And that's X men times fo times two hours equals forty eight man hours. [543] That's man hours. [544] Okay. [545] Divide each side of your equation by two hours. [546] X men is equal to forty eight man hours. [547] Over two hours. |
| Ian (PS25R) |
[548] Yeah. |
| John (PS25P) |
[549] Right. |
| Ian (PS25R) |
[550] I see that. |
| John (PS25P) |
[551] The hours go Oh lovely. [552] Thanks very much . |
| Unknown speaker (FY9PSUNK) |
[553] Do you want that window shut? |
| John (PS25P) |
[554] I'm fine as long it's not too noisy for you . |
| Unknown speaker (FY9PSUNK) |
[555] Are you sure? [556] If No I'm thinking of you you know erm |
| John (PS25P) |
[557] Great fine okay. |
| Unknown speaker (FY9PSUNK) |
[558] if you want to shut it anyway just get up okay . |
| John (PS25P) |
[559] Thanks. [560] Yeah. [561] No I like the fresh air. [562] Okay so the hours would cancel off there. [563] How many twos in that? |
| Ian (PS25R) | [...] |
| John (PS25P) |
[564] Twenty four. [565] So you take twent twenty four men to do the job in two hours . |
| Ian (PS25R) |
[566] In two hours. |
| John (PS25P) |
[567] Now how many man hours would we use up, if we had twenty four men working for two hours? [568] We'd have twenty four |
| Ian (PS25R) |
[569] Forty eight. |
| John (PS25P) |
[570] That's it. [571] Twenty four times two, man hours. [572] So any of th this is a very common problem that you get. [573] So many men digging a ditch, building a wall, digging a hole, whatever it is. [574] And you just, they always tell you, so many men take so long to do it. [575] Well how many man hours. [576] So try one completely on your own. [577] I won't say a word this time. [578] I ant you to do the lot. [579] And I'll turn that over so you can't see that. |
| Unknown speaker (FY9PSUNK) | [laugh] |
| John (PS25P) |
[580] Okay? [581] Erm and I want you to tell me what you're thinking and how you're going through it and [...] So let's see if I can find one of those. [582] Er here we are, the first one here. [583] Fifteen men can build a wall in six hours. [584] Oh it's too easy this cos you can do it in your head. [585] Erm ... right this is better. [586] Four men can build a shed in nine hours. [587] Okay? [588] How long would it take six men? [589] ... [whispering] Keep going. [] |
| Ian (PS25R) |
[590] [whispering] Alright. [591] Nine hours. [] [592] Erm ... Four divide by nine, multiplied by six. |
| John (PS25P) |
[593] Okay. [594] Now that's that's just sort of coming out with the answer. [595] I'm not saying whether it's right or wrong, but how did you get to it? |
| Ian (PS25R) |
[596] Because, I want to find out how many men it'd take you to do the job in one hour. [597] It's not that. |
| John (PS25P) |
[598] Yes. [599] Yeah. [600] That's one way of looking at it. [601] How many men would you take to do the job in one hour sort of thing is you're working out how many man hours th are there in this job. [602] Okay, you just multiply the number of men, times the number of hours, and that gives you the man hours. [603] And that doesn't change. [604] That's always fixed. [605] You always need so many man hours to do it. [606] So wh wh how many man hours are there in that job? |
| Ian (PS25R) |
[607] Four times nine. |
| John (PS25P) |
[608] Right. [609] Four times nine man hours to do the job. [610] ... So how many hours So that comes to? |
| Ian (PS25R) |
[611] Thirty six. |
| John (PS25P) |
[612] Yeah. [613] Thirty six man hours in this job. ... |
| Ian (PS25R) |
[614] Okay. |
| John (PS25P) |
[615] And how many hours would six men have to work for before they worked thirty six man hours? [616] ... If six men worked for one hour, they's work six man hours wouldn't they. [617] If they worked for if six men worked for two hours they'd work |
| Ian (PS25R) |
[618] Six hours. |
| John (PS25P) |
[619] for Right. [620] Six hours. [621] So if mix six men work for six hours, they'll produce thirty six man hours. [622] Which is what we want. [623] Okay. [624] So the way the way of doing it. [625] The men times the hours gives you the man hours. [626] And then you divide that. [627] So same problem now. [628] Six men take nine hours to do it. [629] Ah this is no good, I want this job done erm in four hours. [630] ... How many men are you going to need? ... |
| Ian (PS25R) |
[631] Thirty six and divide that by four |
| John (PS25P) |
[632] Yeah. |
| Ian (PS25R) |
[633] and that'd give you the number of men. |
| John (PS25P) |
[634] Right that's it. [635] And then what will that come to? ... |
| Ian (PS25R) |
[636] Nine men. |
| John (PS25P) |
[637] Yeah. [638] The men times the hours when whenever you whenever you get your answer, you can check that your men times the hours must still still be the same as it was when you when they gave you the question. [639] So if four men take nine hours, nine men will take four hours. [640] Yeah. [641] And they sometimes put it that way round. [642] There was one in erm here where they'd done that. [643] Erm and they did that with the women. [644] Six women take eight hours. [645] How many wonem women would you need to do it in six hours? [646] Well the women times the hours, it takes six times eight women hours to do this. [647] Man hours if you like. [648] It's still gonna take six times eight, but this time the six is the hours so the eight will be women. [649] And doing it on man hours is er an easy way. [650] Erm you probably need to practise a bit. [651] To think of it that way. [652] So that you're not think, Oh You're first thought cos I know the way you you were working, you're thinking Oh if I just double that, half it or take a third of it or something like that. [653] And it doesn't always work out. [654] Sometimes if you get an easy one, fine, you could do it that way. [655] But erm the easi easiest way of the lot is, Well, how much work does this job take? [656] It takes either three men working at ten hours. [657] That gives yo thirty man hours. [658] Or ten men working for three hours, that still gives you thirty men hours. [659] Or fifteen men working for two hours, two men working for fifteen hours. [660] As long as the men time I mean, perhaps it would take sixty men working for half an hour. [661] As long as it comes to the same man hours, then that's it. [662] Cos that's how you measure jobs when you in erm When you're sort of managing projects or something [...] or so many man hours to build this and then so many man hours to do this and then so many man hours to do that. [663] And they always talk about man hours. [664] Erm Do you want to try another one? [665] This time, absolutely no no help at all. [666] I'll just look out the window. [667] But you t say what you're doing. [668] Don't just go for the figures. [669] Come sort of some of the words describe why you're doing what you're doing. [670] Cos it'll help you to erm say what you're doing, and probably to write it down, some of it as well. [671] Rather than just go [...] don't forget if you write it down and you've got the right method. [672] If you get the answer wrong, you can still get some marks. [673] But if you don't write anything down apart from just the answer. [674] If you just put the figures in the calculator and write it down and it's wrong or this one times that one [...] . [675] Erm did we do that one? [...] |
| Ian (PS25R) |
[676] Yeah. |
| John (PS25P) |
[677] We did that one. [678] Okay. [679] [reading] A farmer employs twelve men [] So number number seven. [680] [reading] Twelve men will take ten days, how long would five men take? [] ... |
| Ian (PS25R) |
[681] Twelve men ... Twelve men times ten days. [682] A hundred and twenty |
| John (PS25P) |
[683] Man days. |
| Ian (PS25R) |
[684] man days. |
| John (PS25P) |
[685] That's it ... |
| Ian (PS25R) |
[686] [...] erm How long would it have taken five men? [687] A hundred and twenty divided by the five men. |
| John (PS25P) |
[688] That's it. [689] ... So a hundred and twenty over five men. [690] Right. [691] Will take five days. |
| Ian (PS25R) |
[692] Yeah. |
| John (PS25P) |
[693] Sorry will take [...] |
| Ian (PS25R) |
[694] No. [695] Yeah any |
| John (PS25P) |
[696] [...] Yeah will take five days. [697] ... [...] when you multiply that one by that one, it's got to come to a hundred and twenty man days again. |
| Ian (PS25R) |
[698] Yeah. |
| John (PS25P) |
[699] Cos that never changes the does it. [700] Erm have a go at this one. [701] Erm eight men Is this one you've done? |
| Ian (PS25R) |
[702] No er well I |
| John (PS25P) |
[703] Okay try try it this way with the man hours anyway. [704] Erm or the man days in this case. [705] Eight men take six days. [706] ... [...] how long would twelve Right. [707] Go on. [708] Good. [709] That's excellent. [710] You don't go on to the next bit till you've worked that one out. [711] Erm and a lot of the time you don't need to multiply it out. [712] It's it's better for the working if you just you know show what you're going to do there. [713] That's it. [714] Eight times six man days. [715] Now even if you put that in your calculator and you get it wrong, and you get fifty or something. [716] Then you're going to get a lot of the marks for it, because they can show |
| Ian (PS25R) |
[717] Yeah. |
| John (PS25P) |
[718] that's what you mean. [719] So |
| Ian (PS25R) |
[720] Right. [721] So long would it take [...] twelve men. [722] [whispering] eight six [] Twelve men. ... |
| John (PS25P) |
[723] Okay. [724] ... Now you've got your you've got your twelve |
| Ian (PS25R) |
[725] Now I'm stuck here. |
| John (PS25P) |
[726] Right okay. [727] It's now now we've switched round differently. [728] There we were sort of trying to find out how many men. [729] But here we know how many men ... take how many days? [730] ... And it's this this thing here. [731] But it's that's how many days they took. [732] ... Because how many man days will it be now? [733] It'll be twelve men times |
| Ian (PS25R) |
[734] Yeah. |
| John (PS25P) |
[735] that many days. [736] And the twelves'll cancel and you'll finish up with eight by six again. [737] [...] eight times six. [recording ends] |