11. Two people start from $\mathrm{AB}$ at the same time, heading towards each other. Person A travels at 12.5 kilometers per hour, and Person B travels at 10 kilometers per hour. After 30 minutes, Person A reaches the entrance of Hang Seng Bank and realizes they forgot their credit card, so they return to $\mathrm{A}$ at the same speed to get the card. After retrieving the card, Person A heads back to $\mathrm{B}$ at the same speed. As a result, when Person B reaches $\mathrm{A}$, Person A still needs 15 minutes to reach $\mathrm{B}$. What is the distance between $\mathrm{A}$ and $\mathrm{B}$ in centimeters?
【Analysis】Person A spent half an hour arriving at the Hang Seng Bank entrance, and returned at the same speed, so it took another half an hour to return to point A. Adding the half an hour spent looking for the card, when A set off again, B had already been walking for 1.5 hours.
Assuming B took a total of \( t + 1.5 \) hours to travel from point B to point A,
then A would take \( t \) hours plus 15 minutes, or \( t + \frac{1}{4} \) hours, to travel from point A to point B. This can be expressed in the equation:
\[ 10(t + 1.5) = 12.5 \left( t + \frac{1}{4} \right) \]
Solving for \( t \) gives \( t = \frac{19}{4} \).
Therefore, the distance between A and B is \( 12.5 \left( \frac{19}{4} + \frac{1}{4} \right) = 62.5 \) kilometers.