12. (12 points) Person A and Person B start from points $A$ and $B$ respectively at the same time, walking back and forth between $A$ and $B$; at the same time Person A starts, Person C also departs from $A$ to $B$. When Person A and Person B meet for the first time at point $C$, Person C is still 100 meters away from $C$; when Person C reaches $C$, Person A has walked an additional 108 meters; when Person C arrives at $B$, Person A and Person B meet for the second time. What is the distance between points $A$ and $B$ in meters?
【Solution】Solution: When Jia walks from $A$ to $C$, Bing walks $100 \div \frac{108-100}{100}=1250$ (meters), the distance of $A C$ is $1250 \times \frac{108}{100}=1350$ (meters), the sum of Jia and Yi's speeds is 3 times Bing's speed, then Yi's speed is $(3-108)$ times of Bing's, the distance of $B C$ is $1250 \times\left(3-\frac{108}{100}\right)=2400$ (meters), so the distance of $A B$ is $1350+2400=3750$ (meters). Answer: The distance between $A$ and $B$ is 3750 meters.