A tank can be filled by two inlet pipes in 18 minutes and 15 minutes respectively. There is also an outlet pipe that can drain the tank completely in 45 minutes. If all three pipes are opened simultaneously when the tank is empty, how long will it take to fill the tank?

Explanation

The combined filling rate of the two inlet pipes per minute is 1/18 + 1/15. The outlet pipe empties the tank at a rate of 1/45 per minute. Therefore, the net filling rate is (1/18 + 1/15) - 1/45 = (5/90 + 6/90) - 2/90 = 9/90 = 1/10 of the tank per minute. Hence, the tank will be filled in 10 minutes.