13.103. From the railway station to the tourist base, one can walk along the highway or a path, with the path being 5 km shorter. Two friends agreed that one would walk along the highway at a constant speed of $\mathrm{v}$ km/h, while the other would take the path at a speed of 3 km/h. The second one arrived at the tourist base 1 hour earlier than the first. Find the distance from the station to the tourist base along the highway and the speed $v$ of the first friend, given that $v$ is an integer.
Solution.

Let $x$ km be the distance from the station to the tourist base by road, and $x-5$ km by trail. According to the problem, $\frac{x}{v}-\frac{x-5}{3}=1$, from which $x=\frac{2 v}{v-3}$. The expression makes sense for $v>3$. By trial, we find: at $v=4$ km/h, $x=8$ km. Other solutions to this equation do not satisfy the condition $x-5>0$.

Answer: 8 km, 4 km/h.