Two pipes, P and Q, can fill a tank in 18 minutes and 24 minutes respectively. If both pipes are opened together, after how many minutes should pipe P be closed so that the tank is exactly full at 12 minutes?

Explanation

Let the time pipe P is open be x minutes. Pipe P fills the tank at a rate of 1/18 per minute, and pipe Q at 1/24 per minute. The total work done is: (x/18) + (12/24) = 1. Solving for x gives x = 9 minutes, so pipe P must be turned off after 9 minutes.