1. Petya and Vasya competed in a 60 m race. When Petya finished, Vasya was 9 m behind him. During the second race, Petya started exactly 9 m behind Vasya. Who finished first in the second race and by how many meters did he outpace his opponent? (Assume that each boy ran at the same constant speed both times).
Answer: Petya outpaced Vasya by 1.35 m.

Solution. In the second race, Petya will eliminate the lag from Vasya by running 60 m (Vasya will run 51 m during this time). 9 m remain to the finish line - which is $20 / 3$ times less than at the start of the 1st race. Therefore, the lead will also be $20 / 3$ times less, i.e., $9 \cdot \frac{3}{20}=1.35$ m.

Evaluation. Full solution is worth 11 points.