There is a good reason why experienced folks always measure distances in hours, not miles when traveling on foot. The mileage itself is just meaningless in difficult terrain.

3mph is doable on a day trek if you're very fit, travel light and the terrain is flat and clear (well marked trail or road). In heavily wooded but not too hilly terrain 2mph is a good daily average for a fit man. Add any major slopes however and the time required becomes much more difficult to calculate. Even Naismith's rule is not that accurate. I've seen a chart somewhere that seemed closer to my own experience, I think it was devised by some Swiss mountain climber but I can't remember the details off hand.

Anyway, weather and climate are two other major factors to consider. In general, I believe any healthy person should be capable of covering at least 15 miles in one day, carrying a moderately heavy load over reasonably flat ground. Anyone who can't accomplish that is seriously out of shape and should focus on improving his fitness first. Keep in mind that in a bug out situation motorized transport simply might not be available and if that happens, going on foot will be the only option.