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

Explanation

1. 01

   Each 2-hour round fills $\frac{1}{4} + \frac{1}{6} = \frac{5}{12}$; two rounds, 4 hours, fill $\frac{10}{12}$.

2. 02

   A then fills the last $\frac{2}{12} = \frac{1}{6}$ at $\frac{1}{4}$ an hour in $\frac{2}{3}$ hour: $4\frac{2}{3}$ hours in all.