A pipe fills a tank in 4 hours, and an outlet empties the full tank in 6 hours. If both are open, how long does the empty tank take to fill?

Explanation

1. 01

   The outlet works against the pipe: net rate $= \frac{1}{4} - \frac{1}{6} = \frac{3 - 2}{12} = \frac{1}{12}$ of the tank an hour.

2. 02

   So it fills in 12 hours.