10. (12 points) Three people, A, B, and C, start from the same point on a circular track with a circumference of 360 meters: A starts first, running counterclockwise; before A completes one lap, B and C start simultaneously, running clockwise; when A and B meet for the first time, C is exactly half a lap away from them; after some time, when A and C meet for the first time, B is also exactly half a lap away from them. If B's speed is 4 times that of A, then when B and C start, A has already run $\qquad$ meters.
【Solution】Solution: When A and B meet for the first time, C is exactly half a lap away from them; after a while, when A and C meet for the first time, B is also exactly half a lap away from them.

Therefore, after A and B meet for the first time, A and B continue to run one and a half laps, and B and C are half a lap apart, that is: A and B run: $360+\frac{1}{2} \times 360=540$ meters, A and C together run: $\frac{1}{2} \times 360=180$ (meters), so, A runs $540 \times \frac{1}{5}=108$ (meters), B runs $540-108=432$ (meters), C runs $180-108=72$ (meters),
Therefore, B's speed is $\frac{432}{72}=6$ times that of C,
That is: C's speed is $\frac{2}{3}$ of A's,
$$
\begin{array}{l}
180 \div\left(4-\frac{2}{3}\right)=54 \text { (meters), } \\
360-5 \times 54=90 \text { (meters) }
\end{array}
$$

Answer: When B and C start, A has already run 90 meters,
The answer is: 90