SOLUTION: If 4 men with 9 boys can do a piece of work in 6/5 days, and 3 men with 6 boys can do the same work in 12/7 days, how long would 1 boy alone take to do the work?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: If 4 men with 9 boys can do a piece of work in 6/5 days, and 3 men with 6 boys can do the same work in 12/7 days, how long would 1 boy alone take to do the work?      Log On


   



Question 478463: If 4 men with 9 boys can do a piece of work in 6/5 days, and 3 men with 6 boys can do the same work in 12/7 days, how long would 1 boy alone take to do the work?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let 1/b = part of the work done by one boy in one day, and
let 1/m = part of the work done by one man in one day.
Then %286%2F5%29%284%2Fm+%2B+9%2Fb%29+=+1, and
%2812%2F7%29%283%2Fm+%2B+6%2Fb%29+=+1.
==> 4%2Fm+%2B+9%2Fb+=+5%2F6 and 3%2Fm+%2B+6%2Fb+=+7%2F12
==> 1%2Fm+=+7%2F36+-+2%2Fb from the 2nd equation.
==> 4%287%2F36+-+2%2Fb%29+%2B+9%2Fb+=+5%2F6
==> 7%2F9+-+8%2Fb+%2B+9%2Fb+=+5%2F6 ==> 1%2Fb+=+5%2F6+-+7%2F9 ==>1%2Fb+=+1%2F18
==> 1/18 of the work is done per boy per day.
==> It will take 18 days for one boy to finish the work.