20. (3 points) The PLA soldiers need to repair a dam while the flood continuously destroys it. If 10 people need 45 minutes, and 20 people need 20 minutes, then 14 people need $\qquad$ minutes to repair the dam.
【Solution】Solution: Assume each person repairs 1 unit of the dam per minute, and the flood destroys the dam at a rate of:
$$
\begin{aligned}
& (10 \times 45-20 \times 20) \div(45-20) \\
= & (450-400) \div 25 \\
= & 50 \div 25 \\
= & 2 \text { (units) }
\end{aligned}
$$

The original units of the dam:
$$
\begin{array}{l}
45 \times 10-2 \times 45 \\
=450-90 \\
=360 \text { (units) }
\end{array}
$$
The time required for 14 people to repair the dam:
$$
\begin{array}{l}
360 \div(14-2) \\
=360 \div 12 \\
=30 \text { (minutes) }
\end{array}
$$

Answer: 14 people need 30 minutes to repair the dam.
Therefore, the answer is: 30.