2. Two points are moving along a circle. When moving in the same direction, the faster point catches up with the slower point every 16 seconds. If they move in opposite directions at the same speeds, they meet every 4 seconds. It is known that when moving towards each other along the circle, the distance between the approaching points decreases by 64 cm every 2 seconds (until the moment of meeting). Find the speed of the faster point (in cm/sec).
# Solution:

Let $v-$ be the speed of the faster point, and $u-$ be the speed of the slower point. According to the problem, we set up the system of equations: $\left\{\begin{array}{l}(u+v) \cdot 4=(v-u) \cdot 16 \\ (u+v) \cdot 2=64\end{array} ;\left\{\begin{array}{l}3 v=5 u \\ u+v=32\end{array} ;\left\{\begin{array}{l}u=12 \\ v=20\end{array}\right.\right.\right.$. The speed of the faster point is 20 cm/sec.

Answer: 20.