11. (12 points) Person A and Person B start from point A to point B at the same time: A is faster than B. After A reaches point B, A's speed doubles and A immediately returns to point A, meeting B 240 meters away from point B; after B meets A, B's speed also doubles, and B turns around to return; when A returns to point A, B is still 120 meters away from point A. What is the distance between points A and B in meters?
【Solution】Solution: According to the problem, we have the following diagram:
B
$\qquad$
A
D
$\mathrm{C}$
B
$A D=120$ meters, $B C=240$ meters;
Assume that Jia and Yi meet for the first time at point $C$, then $B C=240$ meters.
According to the problem, if Jia returns from point $B$ at the same speed, the distance difference between Jia and Yi is $240+120=360$ meters;
When Jia and Yi meet at $C$ and then both return to $A$, both of their speeds are doubled, the distance ratio remains the same, and the distance difference is 120. This indicates that when Yi walks from $A$ to the $C$ position, the distance difference between Jia and Yi is 360, and when Yi returns to point $D$, the distance difference is 120. Therefore, the return journey is $\frac{1}{3}$ of the total distance.
The distance $A C$ is: $120 \div\left(1-\frac{1}{3}\right)=180$ (meters);
The total distance $A B$ is: $180+240=420$ (meters);
Therefore, the answer is: 420