Question 71096
It doesn't necessarily take three hours for all three pipes to fill the pool. To solve this problem, let's take pipe 3 as our starting point.  To fill the pool, pipe 3 working alone would take 1/x time.  Since pipe 1 takes 1/3rd the time, it would be represented by 1/1x/3.  Likewise, pipe 2 would be 1/1x/2. To fill one pool our equation would be: 1/x + 2/x + 3/x = 1 whole pool. X(1/x + 2/x + 3/x) = (1)X.  1 + 2 + 3 = X, or X = 6 hours for one whole pool.  The other times are 1/2 * 6, or 3 hours, and 1/3 * 6, or 2 hours to fill a pool.  Checking: 1/2 + 1/3 + 1/6 = 1.