Rationale of the altitude*3 theory

[Easy Street]

But if you do have access to your groundspeed, which is pretty typical in the GPS era, it's a simple calc:

Rate of descent to lose 4500ft in 20nm?
1) Check groundspeed. Let's say 360kts for this example.
2) 360kts = 6nm / min, therefore 20nm = approx 3 mins
3) 4500ft / 3 mins = 1500 fpm required descent rate

It's better to round down at step 2, whether climbing or descending, to ensure that you reach your required altitude before using up the specified distance. This method can be used during a climb to quickly answer questions from ATC such as "can you be at FLXXX by point YYYYY", although you need to make a sensible assessment of how much your rate of climb will diminish as altitude increases.