This leak can empty a full tank in 16 hrs. When the tank is full, a tap is opened into the tank which intakes water at rate of 6 L per hour and because of that the tank is now emptied in 24 hr. What is the capacity of the tank? Let V be the capacity of the tank in litres. The leak can empty a full tank in 16 hours. This means the rate of the leak is V/16 litres per hour (working negatively, removing water). A tap adds water at a rate of 6 L per hour (working positively). When the tank is full and both leak and tap are active, the tank empties in 24 hours. This means the net rate of change of water volume is negative. Net rate = Rate of tap - Rate of leak = 6 - V/16 L/hr. Since the tank empties, the net rate is negative (6 - V/16 6, or V > 96). The time taken to empty the tank from full is Volume / |Net Rate|. 24 = V / (V/16 - 6) (since V/16 - 6 is positive when emptying is written as a positive time). 24 = V / ((V - 96)/16) 24 = 16V / (V - 96) 24(V - 96) = 16V 24V - 24 96 = 16V 24V - 2304 = 16V 24V - 16V = 2304 8V = 2304 V = 2304 / 8 = 288. The capacity of the tank is 288 litres.