13.261. At noon, a pedestrian and a cyclist set out from point $A$ to point $B$, and at the same time, a horseback rider set out from $B$ to $A$. All three started their journey simultaneously. After 2 hours, the cyclist and the horseback rider met 3 km from the midpoint of $A B$, and another 48 minutes later, the pedestrian and the horseback rider met. Determine the speed of each and the distance $A B$, given that the pedestrian moves at half the speed of the cyclist.
Solution.

Let $v_{1}$ km/h be the pedestrian's speed, $2 v_{1}$ km/h be the cyclist's speed, $v_{3}$ km/h be the horse rider's speed, and $x$ km be the distance $A B$.

According to the problem, $\left\{\begin{array}{l}2 v_{1} \cdot 2+2 v_{3}=x, \\ 2.8 v_{1}+2.8 v_{3}=x, \\ 2 v_{3}=\frac{x}{2}-3, \\ 2 v_{1} \cdot 2=\frac{x}{2}+3,\end{array}\right.$

from which $v_{1}=6$ km/h;

$2 v_{1}=12 \mathrm{km} / \mathbf{h} ;$

$v_{3}=9 \mathrm{km} / \mathrm{h} ;$

$x=42$ km.

Answer: 6, 9, and 12 km/h; 42 km.