13.127. At the trainer's signal, two ponies simultaneously started running uniformly along the outer circumference of the circus arena in opposite directions. The first pony ran slightly faster than the second, and by the time they met, the first pony had run 5 m more than the second. Continuing their run, the first pony reached the trainer, who remained in the place from which the ponies started, 9 s after meeting the second pony, while the second pony reached the trainer 16 s after their meeting. What is the diameter of the arena?
## Solution.

Let $x$ m be the distance run by the second pony until the meeting, and $x+5$ m - the first pony. Then the length of the entire arena $\pi d=2 x+5$. The speed of the first pony is $\frac{x}{9}$ m/s, and the second is $-\frac{x+5}{16}$ m/s. According to the condition $9 \frac{x+5}{x}=16 \frac{x}{x+5}$, from which $x=15$, $l=\pi d=35$ m. From this, $d=\frac{l}{\pi} \approx 11 \mathrm{m}$.

Answer: $\approx 11 \mathrm{m}$.