13.123. The motorcyclist was delayed at the barrier for 24 minutes. After increasing his speed by $10 \mathrm{km} / \mathrm{h}$, he made up for the delay on an 80 km stretch. Determine the motorcyclist's speed before the delay.
Solution.

Let $x$ km/h be the motorcyclist's speed before the delay, and $x+10$ km/h on the segment. Without the delay, the motorcyclist would have traveled 80 km in $t$ hours,
but he traveled 80 km at a speed of $x+10$ km/h in $t-0.4$ hours. Then $\left\{\begin{array}{l}(x+10)(t-0.4)=80, \\ x \cdot t=80,\end{array}\right.$

Answer: 40 km/h.