10. (12 points) In a city, from 7:00 to 8:00 in the morning is the peak hour, during which all vehicles travel at half their original speed. Every morning at 6:50, two people, A and B, start from points $A$ and $B$ respectively, heading towards each other, and meet at a point 24 kilometers away from $A$. If B starts 20 minutes earlier, they will meet at a point 20 kilometers away from $A$; if A starts 20 minutes later, they will meet exactly at the midpoint of $A B$. Therefore, the distance between $A$ and $B$ is $\qquad$ kilometers.
【Solution】Solution: If A starts 20 minutes later, then the distance B has traveled is 10 minutes at high speed and 10 minutes at low speed, which can be considered as the distance of 15 minutes at high speed.
$$
\begin{array}{l}
15 \div 20=\frac{3}{4} \\
24-(24-20) \times \frac{3}{4} \\
=24-4 \times \frac{3}{4} \\
=24-3 \\
=21 \text { (km) } \\
21 \times 2=42 \text { (km) }
\end{array}
$$

Answer: The distance between A and B is 42 km.
Therefore, the answer is: 42.