Answer
Pipe A takes 4 hours, and Pipe B takes 12 hours.
Work Step by Step
Let t be the time it takes Pipe A. Thus:
$ 1/ 3 = \frac{1}{t} + \frac{1}{t+8} $
We create common denominators to obtain:
$ .33 = \frac{t+t+8}{t(t+8)} \\ .33t^2 + 2.67t = 2t +8 \\ .33t^2 +.67t -8 = 0 \\ t^2 +2t -24 = 0 \\(t+6)(t-4) =0$
Since t can't be negative, we see that it takes Pipe A 4 hours. This means it takes Pipe B 4+8=12 hours.
