9.1. From points A and B towards each other with constant speeds, a motorcyclist and a cyclist started simultaneously from A and B, respectively. After 20 minutes from the start, the motorcyclist was 2 km closer to B than the midpoint of AB, and after 30 minutes, the cyclist was 3 km closer to B than the midpoint of AB. How many minutes after the start did the motorcyclist and the cyclist meet
Answer: In 24 minutes.

Solution: In 10 minutes, the motorcyclist travels $1 / 4$ of the distance from A to B plus 1 km, while the cyclist travels $1 / 6$ of the distance from A to B minus 1 km. Therefore, in 10 minutes, both of them, moving towards each other, cover $1 / 4 + 1 / 6 = 5 / 12$ of the distance from A to B. This means they will cover the distance from A to B, that is, meet, in $10 * 12 / 5 = 24$ minutes.

Grading Criteria. Correct answer with verification: 3 points. Correctly formulated system of equations: 3 points.