7.7. Cities $A$ and $B$ are located on a river 10 km apart. Which will take the steamboat more time: to travel from $A$ to $B$ and back, or to travel 20 km on a lake?
7.7. Let the speed of the steamboat be $v$, and the speed of the river current be $w$. If $v \leqslant w$, then the steamboat will not be able to move upstream at all. If, however, $v > w$, then the time required for the journey from $A$ to $B$ and back is

$$
\frac{10}{v+w}+\frac{10}{v-w}=\frac{20 v}{v^{2}-w^{2}}>\frac{20}{v}
$$

while the time required to travel 20 km on a lake is $20 / v$.