Two hoses against an open drain

A paddling pool can be filled by one hose in $20$ minutes or by a second hose in $10$ minutes. With its drain open, a full pool empties in $15$ minutes. Starting empty, with both hoses running and the drain open, how many minutes until the pool is full?

$12$ minutes. Net rate is $\tfrac1{20}+\tfrac1{10}-\tfrac1{15}=\tfrac{3+6-4}{60}=\tfrac1{12}$ pool per minute.