13. (12 points) Two people, A and B, are competing in a shuttle run, starting from point $A$ at the same time, reaching point $B$, and immediately returning. The first one to return to point $A$ wins. A reaches point $B$ first and meets B 24 meters away from point $B$. After the encounter, A's speed is reduced to half of the original speed. B's speed remains unchanged. B catches up with A 48 meters away from the finish line. When B reaches the finish line, how many meters is A away from the finish line ( )?
A. 6
B. 8
C. 12
D. 16
【Solution】Solution: Let the distance between $A$ and $B$ be $x$ meters. Then, when they first meet, the distance covered by Jia is $x+24$ meters, and the distance covered by Yi is $x-24$ meters,

So the speed ratio of Jia to Yi when they first meet is: $(x+24):(x-24)$,
The speed ratio of Jia to Yi when they meet for the second time is: $(x-24-48):(x+24-48)=(x-72):(x-24)$;
Therefore, $(x+24):(x-24)=2(x-72):(x-24)$,
Thus, $x+24=2(x-72)$,
Solving for $x$ gives $x=168$,
That is, the distance between the two places is 168 meters,
So the speed ratio of Jia to Yi when they meet for the second time is:
$$
\begin{aligned}
& (168-72):(168-24) \\
= & 96: 144 \\
= & 2: 3
\end{aligned}
$$

So when Yi reaches the finish line, the distance covered by Jia is:
$$
\begin{aligned}
& (168+24) \times \frac{2}{3} \\
= & 192 \times \frac{2}{3} \\
= & 128 \text { (meters), }
\end{aligned}
$$

Therefore, when Yi reaches the finish line, the distance Jia is from the finish line is:
$$
168-24-128=16 \text { (meters) }
$$

Answer: When Yi reaches the finish line, Jia is 16 meters from the finish line.
So the correct choice is: $D$.