SOLUTION: 4 boys and 10 girls can dig a hole in 5 hours, if the boys works at 5/4th rate at which the girl works, how many boys will be needed to dig the hole in 3 hours.

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 4 boys and 10 girls can dig a hole in 5 hours, if the boys works at 5/4th rate at which the girl works, how many boys will be needed to dig the hole in 3 hours.       Log On


   

Question 1122729: 4 boys and 10 girls can dig a hole in 5 hours, if the boys works at 5/4th rate at which the girl works, how many boys will be needed to dig the hole in 3 hours.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
B, boy's rate
G, girl's rate
RT=W, rate time work

system%28%284B%2B10G%29%2A5=1%2CB=%285%2F4%29G%29

%284%2A%285%2F4%29G%2B10G%29%2A5=1

%285G%2B10G%29%2A5=1

75G=1

G=1%2F75-------one girl can dig 1 hole in 75 hours.

B=%285%2F4%29%281%2F75%29
B=%281%29%2F%284%2A15%29
B=1%2F60---------one boy can dig 1 hole in 60 hours.

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How many boys will be needed to dig the hole in 3 hours?
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n boys;
n%281%2F60%29%2A3=1

n=60%2F3
highlight%28n=20%29