Q:

"In the rest" or "at the rest" when talking about the heart rate?

When talking about the normal heart rate, what is the right sentence? 

The normal heart rate in the rest is 60-100 BPM
The normal heart rate at the rest is 60-100 BPM

A:

Actually, the sentence should be:

The normal heart rate at rest is 60-100 BPM.

"At" is correct, and there is no "the" in front of "rest."
Here's an excerpt from Mayo Clinic, a medical research site, 

Generally, a lower heart rate at rest implies more efficient heart function and better cardiovascular fitness.

