1. A mathematician and a physicist started running on a running track towards the finish line at the same time. After finishing, the mathematician said: "If I had run twice as fast, I would have beaten the physicist by 12 seconds." And after finishing, the physicist said: "If I had run twice as fast, I would have beaten the mathematician by 36 seconds." By how many seconds did the winner beat the second participant?
# Answer: 16.

Solution: Let the time it took the mathematician to run the entire distance be $2 x$ seconds, and the time it took the physicist be $2 y$ seconds. Then, under the condition that the mathematician ran twice as fast, we get $2 y-x=12$. And from the condition that the physicist ran twice as fast, we get $2 x-y=36$. From this, we get $x+y=48$. Then $3 x$ $=84, x=28, y=20$. Therefore, $2 x-2 y=16$.

Criteria. If the solution is incorrect - 0 points.

Only the correct answer - 0 points.

If the system of equations is correctly derived - 3 points.

If there is a computational error - 5 points.

If the solution is correct - 7 points.