Pipes A, B, and C together can fill a tank in 6 hours. After operating all three for 2 hours, pipe C is turned off, and pipes A and B finish filling the tank in 7 more hours. How long will pipe C take to fill the tank by itself?

Explanation

In 2 hours, all three pipes fill 2/6 = 1/3 of the tank. The remaining portion is 1 - 1/3 = 2/3. Pipes A and B together fill this remaining 2/3 in 7 hours, so their combined rate is (2/3) ÷ 7 = 2/21 of the tank per hour. Since A, B, and C together fill the tank in 6 hours, their combined rate is 1/6 per hour. Therefore, pipe C's rate alone is (1/6) - (2/21) = 1/14 of the tank per hour, meaning pipe C alone can fill the tank in 14 hours.