Matias rides his bicycle on the streets around four blocks near his house, arranged as shown in the figure. His ride consists of taking the longest possible route, but he has invented a rule to have more fun, which is: he can pass through the street intersections several times, but he cannot pass more than once on the same street, and he must end his bicycle ride when he can no longer respect this condition. The four blocks are square, each with 100 meters on each side, and the width of the streets is not considered relevant. Starting from the point indicated by $P$ in the figure, what is the longest of these bicycle rides that Matias can make?

![](https://cdn.mathpix.com/cropped/2024_05_01_666a1aec7e447b0a6cbeg-015.jpg?height=326&width=289&top_left_y=1202&top_left_x=1563)
Observe that there are 12 streets, or sides of 100 meters, between the four blocks. There are also four corners, marked with $\star$ in the figure, where three streets meet. Whenever Matias passes through one of these four corners, he uses two of these three streets. Thus, by the rule he imposed on himself, when he returns to one of these four corners, the walk ends. Therefore, in any path he takes, there are at least two of these four corners $\star$ where he did not use all the streets that lead to these corners. Thus, the path of maximum length uses at most 10 streets, or a total of $1000 \mathrm{~m}$. In the figure, we have drawn one of the maximum paths.

![](https://cdn.mathpix.com/cropped/2024_05_01_666a1aec7e447b0a6cbeg-058.jpg?height=368&width=342&top_left_y=1255&top_left_x=1531)