How to detect player car overtake of other cars

I am working on top down racing 2d game. I am working with Unity engine from long time so I am very well aware with most of concepts.

Basically I want to detect overtake of player car with other cars, I know a way using ray casting but as per my assumption it become costly operation and reduce game performance.

So I want some suggestion from you friends. I hope I found some intelligent way from you guys.

I currently do about 300 raycasts per second in my game and I run the game at 300 fps. I have a lot of other things running in the background like AI, physics, particles, general game logic, bullets, etc. Dont worry, a few raycasts dont really hurt performance. They take very little