6.3. Petya, Kolya, and Vasya started simultaneously in a 100-meter race, and Petya came in first. When Petya had run half the distance, Kolya and Vasya had run a total of 85 meters. It is known that the speed of each of the three boys was constant throughout the distance. How many meters in total did Kolya and Vasya have left to run to the finish line when Petya finished? Justify your answer.
Solution: Since the speeds of each of the boys are constant, during the time it takes Petya to run the second half of the distance, Kolya and Vasya together will run the same 85 meters, and in total from the start $2 \cdot 85=170$. They should run 200. Therefore, they have $200-170=30$ meters left to run together.

Answer: 30 meters.

Recommendations for checking:

| included in the work | points |
| :--- | :--- |
| correct and fully justified answer | 7 points |
| obtained an incorrect answer solely due to arithmetic errors | 6 points |
| correctly formulated but unsolved equation (system of equations), solving which leads to the answer | 4 points |
| only special cases are considered (e.g., when Vasya and Kolya have the same speed) AND/OR it is stated that in the remaining time Vasya and Kolya will run the same 85 meters together | 2 points |
| only the correct answer is given without justification (or with incorrect justification) | 1 point |

![](https://cdn.mathpix.com/cropped/2024_05_06_04710447941383789653g-5.jpg?height=431&width=415&top_left_y=204&top_left_x=138)

To the condition

problem 6.4