Problem 1. Buratino, Karabas-Barabas, and Duremar are running along a path around a circular pond. They start simultaneously from the same point, with Buratino running in one direction and Karabas-Barabas and Duremar running in the opposite direction. Buratino runs three times faster than Duremar and four times faster than Karabas-Barabas. After Buratino meets Duremar, he meets Karabas-Barabas 150 meters further. What is the length of the path around the pond?
# Solution:

Let the length of the path be S.

Since Buratino runs three times faster than Duremar, by the time they meet, Buratino has run three-quarters of the circle ($3 / 4$ S), while Duremar has run one-quarter. Since Buratino runs four times faster than Karabas-Barabas, by the time they meet, Buratino has run four-fifths of the circle, while Karabas-Barabas has run one-fifth ($1 / 5$ S).

The distance between the meeting points is 150 meters. We get the equation:

$$
\begin{aligned}
& \frac{3}{4} S + 150 + \frac{1}{5} S = S \\
& S = 3000
\end{aligned}
$$

Answer: 3000 meters.