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13 men and 7 boys can finish a job in 7 days, while 6 boys [#permalink]
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)?

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.

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.