# Task 8.2

A team consisting of Petya, Vasya, and a one-person scooter is participating in a race. The distance is divided into segments of equal length, the number of which is 42, with a checkpoint at the beginning of each. Petya runs a segment in 9 minutes, Vasya in 11 minutes, and on the scooter, either of them can cover a segment in 3 minutes. They start simultaneously, and the time of the last one to finish is recorded at the finish line. The team agreed that one of them will ride the first part of the way on the scooter and run the rest, while the other will do the opposite (the scooter can be left at any checkpoint). How many segments should Petya ride on the scooter to achieve the best time for the team?

## Number of points 7

#
# Answer:

18

Solution

If the time of one becomes less than the time of the other of the boys, then the time of the other will increase, and consequently, the team's time will increase. Therefore, the times of the boys must coincide.

Denoting the number of segments driven by Petya as $x$ and solving the equation:

$3 x + 9(42 - x) = 3(42 - x) + 11 x$, we get $x = 18$.