2. Dima and Seryozha decided to have a competition around a circular lake. They start simultaneously from the same point. Seryozha drives a motorboat at a constant speed of 20 km/h and somehow crosses the lake (not necessarily along the diameter) in 30 minutes. During this time, Dima runs along the shore of the lake for the first 15 minutes at a speed of 6 km/h, and then for the rest of the time, he swims on a boat parallel to Seryozha's trajectory. After arriving simultaneously on the other side of the lake, the boys run towards each other. Throughout the game, the boys run at constant and equal speeds. How long after parting will they meet?
Solution: A trapezoid can be inscribed in a circle only if it is isosceles. The length of the segment resting on a chord of the same length in the same circle is the same. Dima runs 1.5 kilometers along the lake. This means they should run 1.5 kilometers together, at a closing speed of 12 km/h, which is 7.5 minutes. In total, 37.5 minutes will have passed from the moment they parted.

| Criteria for Task Evaluation | Points |
| :--- | :---: |
| The correct answer is obtained with justification | 10 |
| The correct answer is obtained, but the solution is either not fully justified or contains an arithmetic error that does not affect the result | 5 |
| The answer is either incorrect or guessed, with no justification provided | 0 |