144(1172). Two athletes are running on the same closed track. The speed of each is constant, and one takes 5 seconds less than the other to run the entire track. If they start running simultaneously from the same starting line in the same direction, they will be side by side after 30 seconds. How long will it take for them to meet if they start running simultaneously from the same starting line in opposite directions?
Solution. Let $s$ (m) be the length of the closed track, $t$ (s) the time it takes for the first athlete to run the entire track. Then the speed of the first athlete is $\frac{s}{t}(\mathrm{~m} / \mathrm{s})$, and the speed of the second athlete is $\frac{s}{t+5}(\mathrm{m} / \mathrm{s})$.

According to the problem, we set up the equation

$$
30 \cdot \frac{s}{t}-30 \cdot \frac{s}{t+5}=s,
$$

from which $t^{2}+5 t-150=0, t=10$ s. Therefore, the speeds of the athletes are $\frac{s}{10} \mathrm{m} / \mathrm{s}$ and $\frac{s}{15} \mathrm{m} / \mathrm{s}$, respectively, and the desired time is $6 \mathrm{s}\left(s:\left(\frac{s}{10}+\frac{s}{15}\right)=6\right)$.

Answer: 6 s.