Like Flite Idol
*, I'm also a "60-to-1" (or "1-in-60") person myself. Very easy to do in the air, real-time.
Examples of how very simple and user-friendly it is:
10 DME Arc = 1 mile for every 6 degrees of arc, because 60/10 = 6
12 DME Arc = 1 mile for every 5 degrees
15 DME Arc = 1 mile every 4 degrees
20 DME Arc = 1 mile every 3 degrees
etc etc.
You can have those "benchmark figures" stored in your brain for quick recall, and from there, it's very easy to figure (or at least approximate quickly) the number of miles.
For example, a 80-degree journey along the 15 DME arc would be 20 miles (and it only took a brief moment to figure that out, since you already knew that a 15 DME arc gives you 4 degrees per mile, and 4 into 80 = 20).
NB - I don't necessarily add the 30% as mentioned by Flite Idol unless I have a significant headwind -- that extra mileage is a good buffer against unexpected tailwinds in the descent.
Keeps it simple (in line with the KISS principle -- remember that one?
)
Remember also that distances don't have to be figured to the nth decimal in flight. Just make sure you're allowing yourself enough space to get down in time (and not excessively early), but don't waste too many brain-bytes doing complex calculations. If you are on a 13-DME arc, for instance, just use the 12DME figures and adjust a bit. And like N_S_R said re groundspeed, don't forget to consider the overall effect of the winds.
*Flite Idol, how have you been? Still flying with the same company? Hope all is going well with you.