SOLUTION: John paints a house 9 hrs longer than frank. Together they can pain it in 20 hrs. How long does it take frank to paint?

Question 1010694: John paints a house 9 hrs longer than frank. Together they can pain it in 20 hrs. How long does it take frank to paint?
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Call the time it takes Frank, f. Then John takes f+9. The normal setup looks like this:
t/A + t/B = 1
Now plug in and get
20/f + 20/(f+9) = 1
Multiply by f(f+9) and get
20(f+9) + 20f = f(f+9)
20f + 180 + 20f = f^2 + 9f
Now collect like terms and solve...we get
f^2 - 31f - 180 = 0
(f - 36)(f + 5) = 0
f = 36 hours
f+9 = 45 hours
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