Problem 3. Brothers Petya and Vasya decided to shoot a funny video and post it on the internet. First, they filmed each of them walking from home to school - Vasya walked for 8 minutes, and Petya walked for 5 minutes. Then they came home and sat down at the computer to edit the video: they started Vasya's video from the beginning and Petya's video from the end (in reverse direction) simultaneously; at the moment when both brothers were at the same point on the path in both videos, they spliced Petya's video with Vasya's. The resulting video shows Vasya walking from home to school, and then at some point, he suddenly turns into Petya and walks backward home. What is the duration of the resulting video?

$[5$ points]

(I.V. Yashchenko)
Answer: 5 minutes.

Solution: Let's play the resulting video on one monitor, and on the other, play Petya's video in full from the end.
Then the monitors will show different scenes until the brothers meet at the same point on the path, after which they will show the same thing. Therefore, the durations of these two videos are equal.