Answer
It takes Tom 6 hours and Terry 8 hours.
Work Step by Step
Let t be the time it takes Tom. Thus:
$ 1 = 3(\frac{1}{t} + \frac{1}{t+2}) +\frac{1}{t+2} $
We create common denominators to obtain:
$1 = \frac{3(t+2+t)+t}{t(t+2)} \\ \\ 1 = \frac{7t+6}{t(t+2)}$
We cross multiply:
$ 7t + 6 = t^2 + 2t \\ 0 = t^2 -5t -6 \\ (t-6)(t+1)$
Since t can't be negative, we see that it takes Tom 6 hours. This means it takes Terry 2+6 = 8 hours.
