a bathtub can be filled by the hot and cold water pipes in four minutes and, when full, can be emptied by the waste pipe in five minutes. If it is half full and all three pipes are set running, when will the tub be filled?

Answer 1

To fill the whole tub with the water running and the drain open would take

tub/(tub/4 - tub/5)
= 20 minutes

But the tub was already half full, so it would take 10 minutes to fill from the moment it was half-full.