13. (12 points) $A$ and $B$ are two places where a bus is dispatched every 5 minutes, traveling at a uniform speed towards each other, and all buses travel at the same speed; two people, Jia and Yi, start from $A$ and $B$ respectively, traveling towards each other at a uniform speed; 5 minutes after Jia and Yi start, the first bus departs from both places; when Jia and Yi meet, Jia is caught up by the 9th bus from $A$, and Yi is also caught up by the 6th bus from $B$; when Yi arrives at $A$, he is caught up by the 8th bus from $B$, and at this time, Jia is still 21 kilometers away from $B$. What is Yi's speed in kilometers per hour?
27
【Solution】Solution: According to the problem, we have:
Let's assume that A and B meet at point C. Since the speed of the bus is constant, the time from one bus catching up with A (B) to the next bus catching up with A (B) is the same.

First, consider B to C (the meeting point). B is caught up by 6 buses, and from C to A, B is caught up by 2 more buses, indicating that the time from B to C is 3 times the time from A to C.

Therefore, $BC = 3AC$. Since C is the meeting point, B's speed is 3 times A's speed. So when B completes the entire journey, A has completed $\frac{1}{3}$ of the journey.
At this point, A is still 21 kilometers away from B, so the total distance of the journey is $21 \div \left(1 - \frac{1}{3}\right) = \frac{63}{2}$ kilometers.
When A and B meet, A has been caught up by 9 buses, and B has been caught up by 6 buses. The bus that caught up with B started 15 minutes earlier than the bus that caught up with A, which is $\frac{1}{4}$ hour.
Since the meeting point is one of the four equal segments of the entire journey, the bus that caught up with B has traveled half the distance more than the bus that caught up with A, which is $\frac{63}{4}$ kilometers.
Therefore, the speed of the bus is $\frac{63}{4} \div \frac{1}{4} = 63$ kilometers/hour. So the bus takes $\frac{63}{2} \div 63 = \frac{1}{2}$ hour to complete the entire journey. When B reaches A, the 8th bus just catches up. This bus starts when B has already walked for 40 minutes, which is $\frac{2}{3}$ hour. This bus takes $\frac{1}{2}$ hour on the road.
B takes $\frac{2}{3} + \frac{1}{2} = \frac{7}{6}$ hours to travel from B to A.
Therefore, B's speed is $\frac{63}{2} \div \frac{7}{6} = 27$ kilometers/hour;
The answer is: 27