4-7. Along a straight alley, 100 lamps are placed at equal intervals, numbered sequentially from 1 to 100. At the same time, from different ends of the alley, Petya and Vasya started walking towards each other at different constant speeds (Petya from the first lamp, Vasya from the hundredth). When Petya was at the 22nd lamp, Vasya was at the 88th lamp. At which lamp will their meeting occur? If the meeting occurs between two lamps, indicate the smaller number of these two.

![](https://cdn.mathpix.com/cropped/2024_05_06_7d113eccc6d3ed32fb40g-03.jpg?height=485&width=1865&top_left_y=1131&top_left_x=107)
Answer. At the 64th lamppost.

Solution. There are a total of 99 intervals between the lampposts. From the condition, it follows that while Petya walks 21 intervals, Vasya walks 12 intervals. This is exactly three times less than the length of the alley. Therefore, Petya should walk three times more to the meeting point than to the 22nd lamppost, i.e., $21 \cdot 3=63$ intervals. And he will be at the 64th lamppost.