A cyclist covers $21 \mathrm{~km}$ per hour on flat terrain, $12 \mathrm{~km}$ per hour uphill, and $30 \mathrm{~km}$ per hour downhill. The entire $80 \mathrm{~km}$ route took 3 hours and 55 minutes one way and 4 hours and 40 minutes on the return trip. What is the length of the flat, uphill, and downhill sections of the route one way?
Let the flat part of the road be $x \mathrm{~km}$, the uphill part be $y \mathrm{~km}$, and the downhill part be $z \mathrm{~km}$. According to the problem,

$$
\begin{gathered}
x+y+z=80 \\
\frac{x}{21}+\frac{y}{12}+\frac{z}{30}=\frac{47}{12} \\
\frac{x}{21}+\frac{y}{30}+\frac{z}{12}=\frac{14}{3}
\end{gathered}
$$

By eliminating the fractions,

$$
\begin{gathered}
x+y+z=80 \\
20 x+35 y+12 z=1645 \\
20 x+14 y+30 z=1960
\end{gathered}
$$

from which $x=35 \mathrm{~km}, y=15 \mathrm{~km}$, and $z=30 \mathrm{~km}$.