13.081. A motorcyclist set off from point $A$ to point $B$, which is 120 km away from $A$. On the way back, he set off at the same speed, but had to stop for 10 minutes after an hour of travel. After this stop, he continued his journey to $A$, increasing his speed by 6 km/h. What was the initial speed of the motorcyclist, given that he spent as much time on the return trip as he did on the trip from $A$ to $B$?
## Solution.

By the condition $A C=C D$ (Fig. 13.4). We have $A C=\frac{120}{x}$, where $x-$ is the initial speed; $C D=1+\frac{1}{6}+\frac{120-x}{x+6} \Rightarrow \frac{120}{x}=\frac{7}{6}+\frac{120-x}{x+6}$, from which $x=48($ km $/ h)$.

Answer: 48 km $/$ h