A pipe can fill a tank in 30 minutes. After it has been running for 10 minutes, a leak starts at the bottom, and because of it the tank fills 10 minutes later than it should have. How long would the leak alone take to empty the full tank?

Explanation

1. 01

   In the first 10 minutes the pipe fills $\frac{1}{3}$ of the tank.

2. 02

   The remaining $\frac{2}{3}$ should take 20 minutes but takes 30, so the net rate is $\frac{2}{3} \div 30 = \frac{1}{45}$.

3. 03

   Leak = $\frac{1}{30} - \frac{1}{45} = \frac{3-2}{90} = \frac{1}{90}$, so it empties the tank in 90 minutes.