2. Alyosha and Vitya set off from point $N$ to point $M$, the distance between which is 20 km. Unfortunately, they have only one bicycle between them. From $N$, Alyosha sets off on the bicycle, while Vitya starts walking. Alyosha can leave the bicycle at any point along the road and continue on foot. When Vitya reaches this point, he switches to the bicycle. Alyosha's walking speed is 4 km/h, and his cycling speed is 15 km/h. Vitya's walking speed is 5 km/h, and his cycling speed is 20 km/h. At what point should Alyosha leave the bicycle so that they both arrive in $M$ at the same time?
Answer. 12 km from point $N$.

Solution. Let $x$ (km) be the distance from $N$ to the point where Alyosha leaves the bicycle. Then Alyosha will spend $\frac{x}{15}+\frac{20-x}{4}$ hours on the entire journey, and Vitya will spend $\frac{x}{5}+\frac{20-x}{20}$ hours. By setting up and solving the equation, we find $x=12$ (km).

Comment. Only the answer - 1 point. The equation for finding the distance is correctly set up, but not solved - 3 points. An arithmetic error is made in solving the equation, but the rest is correct - 5 points.