Question

Ann cleans an apartment in 12 hours and liz cleans an apportment in 18 hours. How long would it take to clean an appartment together?

Answer 1

If Ann cleans in 12 hours then she cleans $\frac{1}{12}$ of the apartment per hour. Similarly Liz cleans $\frac{1}{18}$ of the appartment per hour. So together then can clean $\frac{1}{12}+\frac{1}{18}=\frac{5}{36}$ of the apartment for hour. Therefor it will take them $\frac{36}{5}=7.2$ hours to clean.

The general formula $R_{c}=\frac{AB}{A+B}$ can be used as a check if needed.