# Tag Archives: cars

## Cars overtaking

While cycling during one of the unseasonably sunny October days, I passed lots of cars on the opposite side of the road, but none seemed to be overtaking me. I wondered: how many more I should expect on one side compared to the other?

Making some unrealistic assumptions: I ride my bicycle at a constant speed of $b$ mph in traffic that is constant, with evenly spaced cars (a poor assumption) travelling at a constant speed $c$ mph (not slowing when they overtake—a realistic assumption, in my experience), the answer is easily calculated.

The unslowing cars approach from behind at a merciless relative speed of $c-b$ mph, and those safely across the central double line zoom past at $c+b$ mph. So, for every car I pass on the opposite side of the road, I would expect to be overtaken $\frac{c-b}{c+b}$ times.  Continue reading