1. If you open the cold water tap, the bathtub will fill up in 10 minutes, if you open the hot water tap, it will take 15 minutes. If you pull the plug, the bathtub will completely drain in 12 minutes. How long will it take to fill the bathtub if you open both taps and pull the plug?

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# Answer: 12 min.

Solution: Let's take one bathtub as a unit of volume. The cold water tap flows at a rate of $1 / 10$ of a bathtub per minute, and the hot water tap flows at a rate of $1 / 15$ of a bathtub per minute. Water drains from the drain hole at a rate of $1 / 12$ of a bathtub per minute. Therefore, the total rate is $1 / 10 + 1 / 15 - 1 / 12 = 1 / 12$, so the bathtub will be filled in 12 minutes.