13.300. The smaller arc between points $A$ and $B$, located on a circle, is 150 m. If the points start moving towards each other along the smaller arc, they will meet after $10 \mathrm{c}$, and if they move along the larger arc, the meeting will occur after $14 \mathrm{c}$. Determine the speeds of the points and the length of the circumference, given that point $A$ can run the entire circumference in the time it takes for $B$ to travel only $90 \mathrm{M}$.
## Solution.

Let $V_{a}$ and $V_{b}$ be the speeds of points $A$ and $B$, and $l$ be the length of the circumference. According to the conditions, we have the system $\left\{\begin{array}{l}10\left(V_{a}+V_{b}\right)=150, \\ 14\left(V_{a}+V_{b}\right)=l-150, \\ \frac{l}{V_{a}}=\frac{90}{V_{b}},\end{array}\right.$

from which $V_{a}=12(\mathrm{m} / \mathrm{s}), V_{b}=3(\mathrm{m} / \mathrm{s}), l=360(\mathrm{m})$.

Answer: 12 m $/$ s and 3 m $/ s ; 360$ m.