at a rate or at the rate?

Question

He was going at a rate of 50 miles per hour.

OR

He was going at the rate of 50 miles per hour.

Which one is the most appropriate grammatically speaking and why?

Answer 1

They are both correct. Generally speaking, which is appropriate depends on the context.

In many contexts, including those you quote, you can use either. The distinction is a subtle one.

For example, it sounds more natural to say:

This device works best at a rate of between 100 and 200 rpm.

Because it can be any rate within that range. But you could use either article in:

This device works best at a/the rate of 100 rpm.

The following example requires the because it refers to a specific rate and context:

The rate at which he was travelling posed a danger to other traffic.

In short, you simply have to decide which article fits your sentence better.