A can finish a piece of work in 12 days and B can finish the same work in 18 days. Working together, how long will they take?

Explanation

1. 01

   Work in one day rather than in whole jobs. A does $\frac{1}{12}$ of the work each day and B does $\frac{1}{18}$.

2. 02

   Together they do $\frac{1}{12} + \frac{1}{18} = \frac{3}{36} + \frac{2}{36} = \frac{5}{36}$ of the work per day.

3. 03

   The whole job therefore takes $\frac{36}{5} = 7.2$ days.