13.282. A communications officer was assigned to arrive at point $B$ from point $A$ by a designated time. The distance between $A$ and $B$ is $s$ km. When the communications officer reached point $C$, located exactly halfway between $A$ and $B$, he calculated that he would be 2 hours late if he continued at the same speed. If, however, he rests for 1 hour at point $C$ and increases his speed by $v$ km/h on the remaining half of the journey, he will arrive at $B$ on time. What was the designated time for the communications officer?
Solution.

Let $x$ be the assigned time, $V^{\prime}$ be the speed of the messenger. According to the problem, we have the system

$$
\begin{aligned}
& \left\{\begin{array}{l}
\frac{S}{V^{\prime}}=x+2, \\
\frac{S}{2 V^{\prime}}+1+\frac{S}{2\left(V^{\prime}+v\right)}=x
\end{array}, \text { from which } x=\frac{v+\sqrt{9 v^{2}+6 v S}}{v}(h) .\right. \\
& \text { Answer: } \frac{v+\sqrt{9 v^{2}+6 v S}}{v} h .
\end{aligned}
$$