A printing machine M can print a batch of posters in 5 hours and an older machine N in 8 hours. Only one machine runs at a time: they take turns for one hour each, and N runs the first hour. How long does the batch take?

Explanation

1. 01

   One two-hour cycle prints $\frac{1}{8} + \frac{1}{5} = \frac{13}{40}$.

2. 02

   3 cycles (6 hours) print $\frac{39}{40}$, leaving $\frac{1}{40}$.

3. 03

   Hour 7 belongs to N, which prints $\frac{1}{8} = \frac{5}{40}$ per hour.

4. 04

   Time for $\frac{1}{40}$: $\frac{1/40}{1/8} = \frac{1}{5}$ hour, so the total is $6\frac{1}{5}$ hours.