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