3. (10 points) A water pool has two drainage taps, $A$ and $B$. When both taps are opened simultaneously, it takes 30 minutes to drain the full pool; if both taps are opened for 10 minutes, then tap $A$ is closed and tap $B$ continues to drain, it also takes 30 more minutes to drain the full pool. How many minutes does it take to drain the full pool if only tap $B$ is opened?
45
【Analysis】Assuming the total work is $1, A, B$ together drain the water in 30 minutes, completing $\frac{1}{3}$ of the work in 10 minutes, and $B$ completes the remaining $\frac{2}{3}$ of the work in 30 minutes. Based on this, we can determine $B$'s work efficiency and proceed to solve the problem.
【Solution】Solution: Assuming the total work is $1, A, B$ together need 30 minutes to drain the water. The combined efficiency of the two water outlets is $\frac{1}{30}$. Working together for 10 minutes, they complete $\frac{1}{30} \times 10 = \frac{1}{3}$ of the total work.
However, $B$ working alone needs 30 minutes to complete $\frac{2}{3}$ of the work,
The efficiency of the $B$ water outlet is: $\frac{2}{3} \div 30 = \frac{1}{45}$,
The time required to open $B$ alone: $1 \div \frac{1}{45} = 45$ (minutes).
Therefore, the answer is: 45.