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13 men and 7 boys can finish a job in 7 days, while 6 boys

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13 men and 7 boys can finish a job in 7 days, while 6 boys [#permalink] New post 22 Jul 2007, 12:08
13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 women can finish the same job in 6 days. In how many days can 1 man, 1 boy and 1 woman working together finish the same job (assume constant rates each for men, women, and boys)?

A)42
B)54
C)21
D)63
E)24

Not sure how to approach this problem.
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 [#permalink] New post 22 Jul 2007, 13:41
While I don't know how to set this up to get an exact answer, it is a good candidate for POE (process of elimination)/ballparking. If you look at the group of men and boys, you have 20 people finishing a job in 7 days at their combined rates. Thus it takes them 140 man/days (or should I say person/days?). Then look at the group of women and boys - it takes them a total of 114 man/days. So the answer should be between 114 and 140 man/days. With three people (the one man, one woman, and one boy), it should take somewhere between 38 and 43 days. The only answer in that range is 42.

Is that the correct answer, BTW?
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 [#permalink] New post 22 Jul 2007, 14:38
13M + 7B = x/7
13W + 6B = x/6

Adding 1 and 2

13M + 13W + 13B = 13x/42

1M + 1B + 1W = x/42

Ans : 42
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 [#permalink] New post 22 Jul 2007, 22:29
13 men + 7 boys finish a job in 7 days --> 1/7 job in 1 day
13 women + 6 boys finish a job in 6 days --> 1/6 job in 1 day

So 13 men + 13 women + 13 boys finish 1/7 + 1/6 job in 1 day = 13/42 job in 1 day = 13 men + 13 women + 13 boys finsih takes 42/13 days to finish 1 job.

Then 1 men + 1 women + 1 boy would take 42 days to finish the job.
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 [#permalink] New post 24 Jul 2007, 17:23
OA is 42 thank you all.
  [#permalink] 24 Jul 2007, 17:23
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13 men and 7 boys can finish a job in 7 days, while 6 boys

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