Two taps can fill a tank individually in 10 minutes and 15 minutes respectively. When a waste pipe is also open, the tank fills completely in 18 minutes. How long does the waste pipe take to empty the full tank on its own?

Explanation

Let the time taken by the waste pipe to empty the tank be x minutes. The filling rates of the two taps are 1/10 and 1/15 per minute, and the combined effective filling rate with the waste pipe open is 1/18 per minute. Using the equation: 1/10 + 1/15 - 1/x = 1/18, solving for x gives 9 minutes.