what is a non-unit rate?

I am not familiar with the terminology used this way.

well, I guess 5 cows per acre would be a unit rate

but
1 cow per 50 cows gives no milk has no units

Here is an example of a "non-unit" rate

If the failures on a particular welding process was on the average one inch per 1000 inches, we would say
failure rate=1inch/1000inches = .001
Notice the units divide out.
We Engineers avoid that, we would read the rate as one inch per thousand inches. But Math guys, and statatisians, and quality control tracking guys will say the rate as one thousandth (no units).

Another reason I was a happy engineer.

right, Damon, that example is correct.

A non-unit rate is a rate that does not compare a quantity to a single unit. It compares a quantity to multiple units, expressing the relationship between two different quantities. To understand non-unit rates, let's consider an example:

Let's say you are traveling by car and you cover a distance of 200 miles in 4 hours. The rate of your travel can be expressed as 200 miles per 4 hours. This is a non-unit rate because we are comparing the distance traveled (200 miles) to the time taken (4 hours).

To calculate a non-unit rate, you divide the quantity of the first item by the quantity of the second item. In this case, you divide the distance traveled (200 miles) by the time taken (4 hours) to get the rate of 50 miles per hour.

So, a non-unit rate provides a comparison between two different quantities, indicating how one quantity changes in relation to the other.