13.145. First, the motorboat traveled 10 km downstream, and then twice that distance - across the lake into which the river flows. The entire trip lasted 1 hour. Find the boat's own speed, if the river current speed is 7 km/h.
## Solution.

Let $v$ km/h be the own speed of the boat. Downstream, the boat traveled $\frac{10}{v+7}$ hours, and on the lake $-\frac{20}{v}$ hours. According to the condition, $\frac{10}{v+7}+\frac{20}{v}=1$, from which $v^{2}-23 v-140=0$, i.e., $v=28$ (km/h).

Answer: 28 km/h.