1003197408

The painter $A$ takes $15$ hours to paint a flat. The painter $B$ takes $12$ hours to paint the same flat and the painter $C$ takes $10$ hours to complete the same task. The painter $A$ starts to paint alone and after $2$ hours joins him the painter $B$. After the next hour the painter $C$ starts to paint with them too. How long will all three painters paint together before completing the work?