Kovaldji A.K.

Vladimir is running on a circular track at a constant speed. There are two photographers standing at two points on the track. After the start, Vladimir was closer to the first photographer for 2 minutes, then closer to the second photographer for 3 minutes, and then closer to the first photographer again. How long did it take Vladimir to run the entire circle?
Let's mark the first and second photographers on the circle with points $A$ and $B$ respectively, and points $C$ and $D$ will denote the midpoints of the arcs connecting $A$ and $B$. Then on the semicircle $C A D$, Vasya is closer to the first photographer, and on the semicircle $C B D$ (marked in bold on the diagram) - closer to the second photographer. According to the problem, he was closer to the second photographer for 3 minutes. Therefore, he runs the entire circle in 6 minutes.

![](https://cdn.mathpix.com/cropped/2024_05_06_7c6a12be356bd13b62cag-03.jpg?height=389&width=400&top_left_y=1349&top_left_x=838)

Answer

In 6 minutes.