SOLUTION: If Pat and Mike can put together a peice of furniture in 15 minutes, and alone it takes Mike 15 minutes longer than Pat to do the same job. How long does it take them individually

Question 355083: If Pat and Mike can put together a peice of furniture in 15 minutes, and alone it takes Mike 15 minutes longer than Pat to do the same job. How long does it take them individually?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
let Pat alone do the job in x minutes
Mike takes x+15 minutes alone.
...
Pat does 1/x of the job in 1 minute
mike does 1/(x+15) of the job in 1 minute
together they will do 1/x+1/(x+15) of the job in 1 minute
= (x+15+x)/(x(x+15))
=2x+15/x(x+15)
they will take x(x+15)/2x+15 minutes = 15
x(x+15)/2x+15 = 15
x^2+15x=15(2x+15)
x^2+15x=30x+225
x^2-15x-225=0
Pat does the job alone in 24.27 minutes
Mike will take 39.27 minutes alone
m.ananth@hotmail.ca
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