1. Petya and Vasya simultaneously set off on scooters towards each other. Exactly in the middle between them is a bridge. The road from Petya to the bridge is paved, while the road from Vasya to the bridge is dirt. It is known that they travel at the same speed on the dirt road, and on the paved road, Petya moves 3 times faster than on the dirt road. Petya reached the bridge in one hour and, without stopping, continued his journey. How long after setting off will he meet Vasya?
Answer: in 2 hours.

Solution. Let the distance to the bridge from the starting positions be $x$. Petya reached the bridge in one hour. Vasya was traveling three times slower, so in one hour he covered the distance $x / 3$. At this moment, the distance between Petya and Vasya became $2 x / 3$, and then they moved at the same speed. Therefore, until they meet, each of them will travel the distance $x / 3$. This is the same distance Vasya covered in the first hour. So, it will take them another hour.