2. Petya runs down from the fourth floor to the first floor 2 seconds faster than his mother rides the elevator. Mother rides the elevator from the fourth floor to the first floor 2 seconds faster than Petya runs down from the fifth floor to the first floor. How many seconds does it take for Petya to run down from the fourth floor to the first floor? (The lengths of the stair flights between all floors are the same).
Answer: 12 seconds.

Solution. Between the first and fourth floors, there are 3 flights, and between the fifth and first floors, there are 4. According to the problem, Petya runs 4 flights 2 seconds longer than it takes his mother to ride the elevator, and 3 flights 2 seconds faster than his mother. Therefore, it takes Petya 4 seconds to run one flight. Then from the fourth floor to the first (i.e., 3 flights), Petya runs down in $4 \cdot 3=12$ seconds.

Grading criteria.

- Correct answer with a complete solution - 7 points.
- Explained that it takes 4 seconds for one flight, and the answer is 4 seconds - 5 points.
- Correct reasoning assuming the distance from the fifth floor to the first is 1.25 times the distance from the fourth floor to the first, and the answer is 16 seconds - 3 points.
- Only the answer - 0 points.