There are two options:
One:
Person one was the first racer, and has passed the last runner for the second time.
Two:
This is impossible. You can't pass the last person, because that means you WERE the last person. So that would mean that person one wasn't participating.
See below for further explanation:
Person A ---> Person B.
Who's the last runner? According to the riddle it's person B. How can that be when person A is about to pass person B? That would make person A the last runner.
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