8.5. In the city of Omsk, a metro has been built, represented by a straight line. On this same line is the house where Nikita and Egor live. Every morning they leave the house for classes at the same time, after which Egor runs to the nearest metro station at a speed of 12 km/h, while Nikita walks along the metro line to another station at a speed of 6 km/h. Despite this, every day Nikita manages to arrive on time for the first lesson, while Egor does not, even though he is not delayed anywhere. Find the greatest possible speed of the metro trains, given that it is constant and equal to an integer. (Assume that the school is located directly on a certain metro station, different from the given ones).
Answer: 23 km/h

Solution: Obviously, this is only possible if the subway train first arrives at the nearest station A, where Egor runs to, and then goes to station B, where Nikita is heading.

Let $v$ be the speed of the subway, $S$ be the distance between two adjacent stations, and $R$ be the distance between this subway train and the nearest station at the moment when Nikita and Egor leave home simultaneously.

Egor does not catch the subway, which means $R / v < (S / 2) / 6$

From this, we get: $S v / 12 - S1 / 10$ hours and does not make it.

The subway takes 4.75 km / 23 km/h = 4.75 / 23 hours to reach station B. Nikita walks to station B in $1.23 / 6$ hours < 4.75 / 23 and makes it!

Criteria: Only the answer - 3 points.

Only a complete example with full justification - 3 points

Deduct 2 points for a correct example without justification.