13.130. Two friends in one boat traveled along the riverbank and returned along the same route 5 hours after departure. The entire trip was 10 km. According to their calculations, on average, it took them as much time to travel 2 km against the current as it did to travel 3 km with the current. Find the speed of the current, the time taken for the trip there, and the time taken for the return trip.
Solution.

Let $v$ km/h be the own speed of the boat, $v_{\text {r. }}$ km/h be the speed of the current. According to the problem, $\left\{\begin{array}{l}\frac{2}{v-v_{\mathrm{T}}}=\frac{3}{v+v_{\mathrm{T}}}, \\ \frac{5}{v-v_{\mathrm{T}}}+\frac{5}{v+v_{\mathrm{T}}}=5,\end{array}\right.$ from which $v_{\mathrm{T}}=\frac{5}{12} \mathrm{km} / \mathrm{h} ; v=\frac{25}{12} \mathrm{km} / \mathrm{h}$.

The time to travel there is $\frac{5}{\frac{25}{12}-\frac{5}{12}}=3$ h, and back - 2 h.

Answer: $\frac{5}{12}$ km/h; 3 and 2 h.