8.2. Petya and three of his classmates started a 100-meter race at the same time, and Petya came in first. After 12 seconds from the start of the race, no one had finished yet, and the four participants had run a total of 288 meters. When Petya finished the race, the other three participants had 40 meters left to run in total. How many meters did Petya run in the first 12 seconds? Justify your answer. It is assumed that each participant ran at a constant speed.
Solution: The runners were supposed to run a total of 400 meters, and in 12 seconds they ran 288 meters, meaning that in 1 second the runners run $288: 12=$ 24 meters. When Petya finished, the runners had run $400-40=360$ meters, so from the start, $360: 24=15$ seconds had passed. Therefore, Petya runs at a speed of $100 / 15$ meters per second, and in 12 seconds he runs $\frac{100}{15} \cdot 12=80$ meters.

Answer: 80 meters.

Recommendations for checking:

| present in the work | points |
| :--- | :--- |
| correct and fully justified answer | 7 points |
| an incorrect answer due solely to arithmetic errors | 6 points |
| the equation (system of equations) is correctly set up but not solved, the solution of which leads to the answer | 4 points |
| only partial cases are considered (e.g., when the speeds of the other three runners are the same) and/or only the sum of the speeds of all 4 runners (24 m/s) is found | 2 points |
| only the correct answer is given without justification (or with incorrect justification) | 1 point |