SOLUTION: It takes Steve 3 hrs longer to paint a floor than it takes Paul. When working together, it takes them 2 hours. How long would each take to do the job alone?

Question 200817: It takes Steve 3 hrs longer to paint a floor than it takes Paul. When working together, it takes them 2 hours. How long would each take to do the job alone?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
It takes Steve 3 hrs longer to paint a floor than it takes Paul. When working together, it takes them 2 hours. How long would each take to do the job alone?
.
Let p = time it takes for Paul to paint the floor alone
then
p+3 = time it takes for Steve to paint the floor alone
.
2(1/p + 1/(p+3)) = 1
2/p + 2/(p+3) = 1
2(p+3) + 2p = p(p+3)
2p+ 6 + 2p = p^2+3p
8p+ 6 = p^2+3p
6 = p^2-5p
0 = p^2-5p-6
0 = (p-6)(p+1)
p = {6, -1}
We throw out the negative solution leaving us with:
p = 6 hours (time it takes Paul)
.
Steve:
p+3 = 6+3 = 9 hours (time it takes Steve)

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