I am modeling HO (1:87) scale trains. A scale mile is approximately 60.68 feet. How long, in real time, should the model take to traverse this distance to cover the distance at a scale 10 MPH, or 30 MPH, and so on. I know there has to be a simple formula for making these calculations, but, I really didn’t pay much attention in math class. Help me out here, please.

I’m guessing .5 MPH to 1.5 MPH
I could be wrong
Hmmmm… gee….. Sorry, I only know how to scale fish, not time.
The model will appear most realistic if you simply don’t scale time. At 10 MPH, it takes 1/10 of an hour = six minutes to traverse a mile. So your model train should traverse the scale mile in 6 minutes. Or 1/30 hour = 2 minutes at 30 MPH.
This is easier in metric units, btw. If the real train goes 20 meter per second, your model train goes 20/87=0.23 meter per second, that is 23 centimeter per second.
If the model is to scale, and it’s traveling a scaled mile, then it would take the same amount of time to travel in 1:87 scale as the full size train does in 1:1 scale.
60 mph = 1 mile per minute or, to scale, 60.68 feet per minute
30 mph = 0.5 miles per minute, 30.34 feet per minute
10 mph = 0.167 miles per minute, 10.1134 feet per minute