Posted by **john** on Monday, July 23, 2012 at 12:13am.

john takes 3hours longer than andrew to peel 400 pounds of apples. if together they can peel 400pounds of apples in 8hours then how long would it take john if he is working alone.

- math -
**Reiny**, Monday, July 23, 2012 at 8:34am
Andrew's rate = 400/x

Johns rate = 400/(x+3)

combined rate = (400(x+3) + 400x)/(x(x+3)

= 400(2x+2)/(x(x+2))

400 / [400(2x+3)/(x(x+3) ] = 8

1/[2x+3)/(x(x+2)) ] = 8

x(x+3)/(2x+3) = 8

x^2+3x = 16x + 24

x^2 - 13x - 24 = 0

x = (13 ±√265)/2

x = 14.64 hrs , ignoring the negative answer

check:

combined rate = 1/14.64 + 1/17.64 = .125

time at comined time = 1/.125 = 8 , Yeahh!

Andrew alone can do it in 14.65 hrs

John alone can do it in 17.65 hrs

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