# 4. Option 1.

Cyclists Alexei, Vitaly, and Sergey participated in a 10 km race. At the moment when Alexei arrived at the finish line, Vitaly had 1 km left to go. And when Vitaly arrived at the finish line, Sergey had 1 km left to go. By how many kilometers did Alexei lead Sergey at the finish line?
Answer: 1.9.

Solution: Vitaly's speed is 0.9 of Alexey's speed, and Sergey's speed is 0.9 of Vitaly's speed, i.e., 0.81 of Alexey's speed. Therefore, when Alexey has traveled 10 km, Sergey has traveled $10 \cdot 0.81 = 8.1$ km. Thus, Alexey is ahead of Sergey by $10 - 8.1 = 1.9$ km.