1. Pete and Vasya competed in a 100 m race. When Pete finished, Vasya was 10 m behind him. During the second race, Pete started exactly 10 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 m.

Solution. In the second race, Petya eliminates the lag from Vasya by running 100 m (during this time, Vasya will run 90 m). 10 m remain to the finish line - 10 times less than at the start of the 1st race. Therefore, the lead will be 10 times less, i.e., 1 m.

Scoring. 11 points for a complete solution.