Two pipes, P and Q, can fill a tank in 12 minutes and 15 minutes respectively. Both pipes are opened simultaneously, but after 3 minutes, pipe P is closed. How much additional time will pipe Q need to fill the tank completely?

Explanation

Pipe P fills the tank at a rate of 1/12 per minute, and pipe Q at 1/15 per minute. Both work together for 3 minutes, filling (3 × (1/12 + 1/15)) = 3 × (9/60) = 9/20 of the tank. The remaining part is 1 - 9/20 = 11/20. Pipe Q alone fills the remaining portion, so time required is (11/20) ÷ (1/15) = 11.25 minutes, which is 11 minutes and 15 seconds.