3. Motorcyclists Vasya and Petya are riding with constant speeds on a circular track 1 km long. Vasya noticed that Petya overtakes him every 2 minutes. Then he doubled his speed and now he himself overtakes Petya every 2 minutes. What were the initial speeds of the motorcyclists? Answer: 1000 and 1500 meters per minute.
Solution. Let Vasya's initial speed be Vv m/min, and Petya's speed be Vp m/min. Then in the first case $1000=2 \cdot(V p-V v)$, and in the second case - 1000=2$\cdot$(2Vv - Vp). Adding these equations, we get $2000=2 \cdot$ Vv. Therefore, Vv $=1000$ m/min, and then Vp=1500m/min.