13.077. The older brother on a motorcycle and the younger brother on a bicycle made a two-hour non-stop trip to the forest and back. During this time, the motorcyclist traveled each kilometer 4 minutes faster than the cyclist. How many kilometers did each of the brothers travel in 2 hours, if it is known that the distance covered by the older brother in this time is 40 km more?
## Solution.

Let $x$ km be the distance the younger brother traveled, and $x+40$ km be the distance the older brother traveled. The younger brother took $\frac{120}{x}$ minutes to travel 1 km, and the older brother took $\frac{120}{40+x}$ minutes. According to the condition, $\frac{120}{x}-4=\frac{120}{40+x}$, from which we get $x=20$.

Answer: 20 and 60 km.