13.280. To control the skier's movement, the coach divided the track into three equal-length sections. It became known that the average speeds of the skier on these three separate sections were different. On the first and second sections combined, the skier took 40.5 minutes, and on the second and third sections - 37.5 minutes. It also turned out that the average speed of the skier on the second section was the same as the average speed for the first and third sections combined. How long did it take the skier to reach the finish line?
## Solution.

Let $x$ be the length of the segment, $t_{1}, t_{2}, t_{3}$ be the time taken to run the first, second, and third segments, respectively. According to the problem, we have the system

$$
\left\{\begin{array}{l}
t_{1}+t_{2}=40.5 \\
t_{2}+t_{3}=37.5, \text { from which } t_{1}+t_{2}+t_{3}=58.5 \text { (min). } \\
\frac{x}{t_{2}}=\frac{2 x}{t_{1}+t_{3}}
\end{array}\right.
$$

Answer: in 58.5 min.