Pipe A fills a tank in 6 hours and pipe B in 4 hours. They are opened by turns, one hour each, starting with A. How long does the tank take to fill?

Explanation

1. 01

   Each pair of hours fills $\frac{1}{6} + \frac{1}{4} = \frac{5}{12}$. After 4 hours, $\frac{10}{12}$ is full.

2. 02

   The rest, $\frac{2}{12} = \frac{1}{6}$, is exactly what A fills in its next hour: 5 hours in all.