Between the ports of Mumraj and Chaos, two ships are plying the same route. They spend a negligible amount of time in the ports, immediately turn around, and continue their journey. One morning, at the same moment, a blue ship sets sail from the port of Mumraj and a green ship from the port of Chaos. For the first time, the ships meet $20 \mathrm{~km}$ from the port of Mumraj, and after some time, they meet again at this very port. By then, the blue ship has already completed the route between the ports four times, while the green ship has only completed it three times.

How long is the route between the ports of Mumraj and Chaos?

(F. Steinhauser)

Hint. Which ship is faster? And by how much?
Ships sail from their ports simultaneously, the place of their first meeting corresponds to their speeds: the ratio of the distances traveled from the ports is equal to the ratio of the respective ship speeds.

The speed ratio of the blue and green ships is $4: 3$. In the same ratio are the distances from the ports Mumraj and Zmatek (in this order). The distance from Mumraj is $20 \mathrm{~km}$, so the distance from Zmatek is $15 \mathrm{~km}(20: 15=4: 3)$.

The route between the ports is $35 \mathrm{~km}(20+15=35)$ long.