Problem 7-3. Midway between points A and B is a coffee shop. A cyclist first set off from A to B. When he was halfway to the coffee shop, a motorist set off from A. It is known that when the motorist arrived at the coffee shop, the cyclist was still on the way between A and B, and the distance between him and the motorist at that moment was half of what it was when the motorist first set off from A. Which event will happen earlier: the cyclist reaching B or the motorist reaching B?
Answer: simultaneously.

Solution. Let the distance $A C$ be 1. When the motorist set off from , the cyclist was at point $1 / 2$, and when he reached - at point $3 / 4$. Therefore, the speed of the car is four times the speed of the bicycle. At this moment, the distance between the cyclist and  was four times less than the distance between the motorist and . Thus, exactly when the cyclist reaches , the motorist will arrive at .

| Rating | Score | Content criterion |
| :---: | :---: | :--- |
| + | 20 | Complete solution |
| $+/-$ | 14 | There is significant progress, but the problem is not brought to an answer |
| $+/ 2$ | 10 | Presence of a correct and incorrect solution |
| - | 0 | The solution is completely wrong/only the answer |