In the first place, I never race, unless it's camel-racing, but I think you are talking about a foot-race. Dare I say?
I think this is what you call a 'logic puzzle'. Am I wrong?
So there is a trick to it.
What's the trick? Obviously if you are in a race and you overtake the other person, you are assuming you are racing against another 'person'. But, let's pause and examine this more closely.
Pass me my magnifying glass...a yes...ah well...now I see! There is some mustard on my tie from the hotdog I had for lunch--those magnifying glasses are great for discovering things like that.
But as to the "puzzle". Let us get back to that. Let us not be distracted from this mental-challenge posed to titillate our little 'grey cells'.
So here's the situation. You have me. You have you. We are racing. But wait, who shot the 'starter's gun'?
There MUST be a third person!
Ah ha! Now I we are getting somewhere.
The mysterious third person. Who is he? Or she? He has a starter's pistol, we know that!
Perhaps they use it to shoot you so that I win the race. They will if I pay them enough. In which case, when I overtake you I am doing it "over your dead body".
So I win. Where's my winners' purse?
What was the question, anyway...