SOLUTION: Gail can build a cabinet in 6 hours. her cousin bobby can build the same cabinet in 15 hours. if they work together, gail works 4 1/2 hours less than bobby, how long does each work

Question 354086: Gail can build a cabinet in 6 hours. her cousin bobby can build the same cabinet in 15 hours. if they work together, gail works 4 1/2 hours less than bobby, how long does each work?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Gail can build a cabinet in 6 hours. her cousin bobby can build the same cabinet in 15 hours. if they work together, gail works 4 1/2 hours less than bobby, how long does each work?
.
Let x = time bobby works
then
x-4.5 = time Gail works
.
x(1/15) + (x-4.5)(1/6) = 1
Multiply both sides by 30:
x(2) + (x-4.5)(5) = 30
2x + 5x - 22.5 = 30
7x - 22.5 = 30
7x = 52.5
x = 7.5 hours (time bobby works)
.
Gail:
x-4.5 = 7.5-4.5 = 3 hours
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