11.1. Arkady, Boris, and Vasili decided to run the same distance, consisting of several laps. Arkady ran each lap 2 minutes faster than Boris, and Boris ran 3 minutes faster than Vasili, and all of them ran at a constant speed. When Arkady finished the distance, Boris had one lap left to run, and Vasili had two laps left. How many laps did the distance consist of? Provide all possible answers and explain why there are no others.
Answer: 6.

Solution: Let the distance be $n$ laps, and Arkady takes $t$ minutes per lap. Then in $n t$ minutes, Arkady runs the entire distance. In this time, Boris runs one lap less, and Vasily runs two laps less. Therefore, $n t=(n-1)(t+2)$ and $n t=(n-2)(t+5)$. From this, it follows that $2 n=t+2$ and $5 n=2 t+10$, so $n=5 n-4 n=(2 t+10)-2 \cdot(t+2)=6$. Note that in this case, $t=10$, and all conditions are satisfied.

Comment: Only the answer - 2 points.

Remark: From the text of the problem, it follows that the problem has at least one solution. Therefore, if it is proven that there can be no other solutions besides $n=6$, it is not necessary to check this solution.