An athlete usually runs $15.5 \mathrm{~km}$ around a rectangular square with dimensions $900 \mathrm{~m} \times 600 \mathrm{~m}$. He always starts the run from point $P$, which is $550 \mathrm{~m}$ from one of the vertices, running in a clockwise direction, as shown in the figure. At what point in the square does he stop?

![](https://cdn.mathpix.com/cropped/2024_05_01_dbce7bc2a200e234c3e2g-02.jpg?height=284&width=441&top_left_y=953&top_left_x=1281)
The distance he covers with each complete lap is equal to the perimeter of the square:

$$
2 \times 900 + 2 \times 600 = 3000 \mathrm{~m}
$$

Since $15.5 \mathrm{~km} = 15500 \mathrm{~m}$ and $15500 = 5 \times 3000 + 500$, the athlete completes 5 full laps (starting from $P$ and returning to $P$), and runs an additional $500 \mathrm{~m}$. Therefore, he stops at point $Q$, $150 \mathrm{~m}$ from vertex $B$, as shown in the figure.

![](https://cdn.mathpix.com/cropped/2024_05_01_dbce7bc2a200e234c3e2g-14.jpg?height=279&width=458&top_left_y=1601&top_left_x=1273)