A crew of rowers travels $3.5 \mathrm{~km}$ downstream and the same distance upstream in a total of 1 hour and 40 minutes in a river. The speed of the river current is $2 \mathrm{~km}$ per hour. How far would the rowing team travel in 1 hour in still water?
1 hour 40 minutes $=\frac{5}{3}$ hours.

If the rowing team travels at a speed of $x \mathrm{~km}$ per hour in still water, then their speed downstream in flowing water is $x+2$, and upstream is $x-2$ (km per hour).

$$
3.5 \mathrm{~km} \text{ downstream takes } \frac{3.5}{x+2}, \text{ and upstream takes } \frac{3.5}{x-2} \text{ hours }
$$

they row, so

$$
\begin{aligned}
\frac{3.5}{x+2}+\frac{3.5}{x-2} & =\frac{5}{3}, \quad \text { or } \quad 3.5(x-2+x+2) \cdot 3=5(x+2)(x-2) \\
3 \cdot 7 x & =5\left(x^{2}-4\right), \quad \text { that is } \quad 5 x^{2}-21 x-20=0
\end{aligned}
$$

From this

$$
x=\frac{21 \pm \sqrt{441+400}}{10}=\frac{21 \pm 29}{10} ; \quad x_{1}=5, \quad x_{2}=-\frac{8}{10}=-\frac{4}{5}
$$

Only $x=5$ satisfies our problem; therefore, the rowing team travels at a speed of $5 \mathrm{~km}$ per hour in still water.