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 a 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.