A tank is being filled by a pipe that alone would fill it in 12 hours. Unnoticed, a leak that alone would empty a full tank in 36 hours is open from the start. Three hours after filling begins the leak is spotted and plugged. How long does the filling take altogether?

Take the tank as 36 units: the pipe gives 3 units an hour, the leak takes 1, so the first three hours gain only 6 units. With the leak plugged, the pipe delivers 3 units an hour and the remaining 30 units take 10 hours. Total 3 + 10 = 13 hours. 12 hours ignores the leak entirely. 18 hours keeps the leak open the whole time (36 ÷ 2). 15 hours adds the pipe's full 12-hour solo time after the plug, forgetting that a sixth of the tank was already in.