1. Andrei, Boris, and Valentin participated in a 1 km race. (We assume that each of them ran at a constant speed). Andrei was 100 m ahead of Boris at the finish line. And Boris was 60 m ahead of Valentin at the finish line. What was the distance between Andrei and Valentin at the moment Andrei finished?
Answer: $154 \mathrm{m}$.

Solution. Let the speeds of Andrey, Boris, and Valentin be $a, b$, and $c \mathrm{m} /$ s, respectively. From the condition, it follows that $b=0.9 a, c=0.94 b$. Therefore, $c=0.9 \cdot 0.94 a=0.846 a$. This means that when Andrey runs 1000 m, Valentin will cover 846 m. The lag will be 154 m.

Evaluation. 12 points for a correct solution.