2. For delivering the mail, the postman uses a bicycle. From the post office to location $A$ is $48 \mathrm{~km}$. The first $10 \mathrm{~km}$ of the route is flat, the next $10 \mathrm{~km}$ is uphill, then $6 \mathrm{~km}$ is flat again, and the remaining part of the route is downhill, inclined at the same angle as the uphill section. On the flat sections, the postman travels at $8 \mathrm{~km}$ per hour, and on the uphill section, he travels at $3 \mathrm{~km}$ per hour. At what speed does the postman ride downhill if it takes him $\frac{14}{5}$ hours longer to return from location $A$ to the post office than it takes to travel from the post office to location $A$?
Solution. Let $x$ be the speed at which the postman drives through the valley. The valley distance from the post office to point $A$ is $48-(10+10+6)=22 \mathrm{~km}$. The postman took $\frac{10}{8}+\frac{10}{3}+\frac{6}{8}+\frac{22}{x}$ hours to travel from the post office to point $A$. The same route from point $A$ to the post office took $\frac{22}{3}+\frac{6}{8}+\frac{10}{x}+\frac{10}{8}$ hours. Therefore, the equation

$$
\frac{10}{8}+\frac{10}{3}+\frac{6}{8}+\frac{22}{x}+\frac{14}{5}=\frac{22}{3}+\frac{6}{8}+\frac{10}{x}+\frac{10}{8}
$$

holds, whose solution is $x=10$. Therefore, the postman's speed through the valley is 10 $km$ per hour.