SOLUTION: I've tried doing the following problem by using an example in the book to no avail. Here is the problem: John takes 3 hours longer than Andrew to peel 500 pounds of apples. If tog

Question 778064: I've tried doing the following problem by using an example in the book to no avail. Here is the problem:
John takes 3 hours longer than Andrew to peel 500 pounds of apples. If together they can peel 500 pounds of apples in 8 hours, then how long would it take each one working alone?
book answer: Andrew takes 14.6 hours and John takes 17.6 hours
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Andrew takes x hours
John takes x+3 hours
Together they take 8 hours
Now consider amount of task completed per hour
Andrew takes 1/x hour
John takes 1/(x+3) hour
together takes 1/8 hour
Adding their labor
(1/x) + (1/(x+3)) = 1/8
(x+3+x) / (x^2 + 3x) = 1/8
cross multiply the fractions
8*(2x+3) = x^2 +3x
16x+24 = x^2 +3x
x^2 -13x -24 = 0
now use the quadratic formula to solve for x
x = (13 + square root (13^2 +4*24)) / 2 = 14.6
x = (13 - square root (13^2 +4*24)) / 2 = -1.6
so we have Andrew takes 14.6 hours and John takes 17.6 hours

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