SOLUTION: After 5 hours of house painting, Jess asked the assistance of Jon. Together, they finished the job in 4 more hours. Had Jon joined in an hour after Jess started working, the job wo

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Question 152452: After 5 hours of house painting, Jess asked the assistance of Jon. Together, they finished the job in 4 more hours. Had Jon joined in an hour after Jess started working, the job would have been finished in 7 hours. How long would it have taken Jess to paint the house alone?
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let x="Jess time alone" and y="Jon time alone"

"After 5 hours of house painting, Jess asked the assistance of Jon. Together, they finished the job in 4 more hours"
__ 9/x+4/y=1 __ 9y+4x=xy __ 4x=xy-9y __ 4x=y(x-9) __ 4x/(x-9)=y

"Had Jon joined in an hour after Jess started working, the job would have been finished in 7 hours"
__ 8/x+7/y=1 __ 8y+7x=xy

substituting __ 8[4x/(x-9)]+7x=x[4x/(x-9)] __ multiplying by x-9 __ 32x+7x^2-63x=4x^2
subtracting 4x^2 __ 3x^2-31x=0 __ factoring __ x(3x-31)=0

x=0 __ not realistic

3x-31=0 __ x=31/3