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July 22, 2014

July 22, 2014

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

- math -
**Reiny**, Monday, July 23, 2012 at 8:34amAndrew'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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