Two pipes, A and B, can fill a tank individually in 10 minutes and 15 minutes, respectively. Both pipes are opened simultaneously, but the tank does not fill as expected because a waste pipe is also open. After noticing this, the person closes the waste pipe, and the tank fills completely in 4 more minutes. How long does the waste pipe take to empty the full tank?

Explanation

The combined filling rate of pipes A and B is 1/10 + 1/15 = 1/6 of the tank per minute. When both pipes and the waste pipe are open, the effective filling rate is reduced. After 4 minutes of filling with only pipes A and B open, 4 × (1/6) = 2/3 of the tank is filled. Therefore, the waste pipe empties the tank at a rate that reduces the filling rate by 1/3 tank per minute. Setting up the equation: (1/10) + (1/15) - (1/x) = 1/3, solving for x gives x = 8 minutes.