2. Usain runs one lap around the school stadium at a constant speed, while photographers Arina and Marina are positioned around the track. For the first 4 seconds after the start, Usain was closer to Arina, then for 21 seconds he was closer to Marina, and then until the finish, he was closer to Arina again. How long does it take for Usain to run a full lap?
# Solution:

It is not hard to see that regardless of Arina and Marina's positions, the entire circle of the school stadium is divided into two equal parts - half of the circle is closer to Arina and the other half is closer to Marina (this is half of the shorter arc between Arina and Marina and half of the longer arc between Arina and Marina - highlighted with a thick line in the diagram on the right). Therefore, the distance Usain covers while being closer to Marina is half of the entire circle. He covers this distance in 21 seconds, so he will cover the entire circle in 42 seconds.

![](https://cdn.mathpix.com/cropped/2024_05_06_8c2afd184a89cceb10e4g-2.jpg?height=408&width=411&top_left_y=1983&top_left_x=1531)

## Criteria:

Correct answer without justification or with incorrect justification - 2 points.

Incorrect justification includes justification based on a specific case of the positions of Arina, Marina, and Usain at the start (for example, if the author places them at opposite points of the circle, with Usain at the midpoint of the arc between them).