13.351. The road from post office $A$ to village $B$ goes uphill for 2 km, then on flat ground for 4 km, and finally downhill for 3 km. The postman takes 2 hours and 16 minutes to travel from $A$ to $B$, and 2 hours and 24 minutes to return. If the final destination of his route were located on the same road but twice as close to $A$, then the total time for the round trip would be 2 hours and 19 minutes. How many kilometers per hour does the postman walk when he is: a) going uphill; b) on flat ground; c) going downhill?
## Solution.

Let $V_{1}, V_{2}, V_{3}$ be the speeds of the postman on the uphill, flat, and downhill sections, respectively. According to the problem, we have the system

$$
\left\{\begin{array}{l}
2 V_{1}+4 V_{2}+3 V_{3}=2 \frac{16}{60} \\
3 V_{1}+4 V_{2}+2 V_{3}=2 \frac{24}{60} \\
2 V_{1}+\left(\frac{2+4+3}{2}-2\right) V_{2}+\left(\frac{2+4+3}{2}-2\right) V_{2}+2 V_{3}=2 \frac{19}{60}
\end{array}\right.
$$

from which $V_{1}=3(\mathrm{km} / \mathrm{h}), V_{2}=4(\mathrm{km} / \mathrm{h}), V_{3}=5($ km $/$ h) .

Answer: a) $3 \mathrm{km} / \mathrm{h} ;$ b) $4 \mathrm{km} / \mathrm{h} ;$ c) $5 \mathrm{km} / \mathrm{h}$.