13.349. From post office $A$ to village $B$, one needs to walk 9 km. The postman walks the entire path there and back, without stopping in the village, in 3 hours and 41 minutes. The road from $A$ to $B$ goes uphill first, then on flat ground, and finally downhill. Over what distance does the road run on flat ground, if the postman walks uphill at a speed of 4 km/h, on flat ground at 5 km/h, and downhill at 6 km/h?
## Solution.

Let $x, y, z$ be the lengths of the road uphill, on flat ground, and downhill, respectively. According to the problem, we have the system

![](https://cdn.mathpix.com/cropped/2024_05_21_3edb7be591bff54ce350g-1216.jpg?height=172&width=969&top_left_y=1315&top_left_x=149)

from which $y=4$ (km).

Answer: 4 km.