The Roman military manual is precise in how far, how much kit they carry and the pace of a centurian. We know this from scholars such as Judson (1888) who researched the roman military historian, Vegetius (Flavius Vegetius Renatus) [0] Vegetius wrote in detail how the Roman military organised itself: [1]

    Kit weight: 30-40lbs (15+kg)
    Pace: 40,000 quick step of 2.5ft at a cadence of 100 to 120 steps/min. 
          (a baseline number still used today in modern Infantry).
    Distance: 15-20miles in seven hours
    Average Speed: 1-3mi/hr depending on terrain, max by road.

Remember this is a minimum distance, moving a lot of people. What happens bumping up the distances up to say 20-30km per day? I've tried this. I bumped up the distances up to 33km/day over multiple days with 10kg weights. It's brutal. I did this to train for a 240km march in 9 days last year. You can see the type of kit we carried http://www.flickr.com/photos/bootload/4665564383/in/set-7215... and terrain traversed ~ http://www.flickr.com/photos/bootload/sets/72157623796441755... before we hit the mountains. Of the 20 that started only 3 finished without injury, including myself.

This is way beyond the ability of most ordinary people. Even 10km with no carry weight. I can say this because I average 2000km/year on foot with average weight of 1-12kg, 10km at a time. I aimed to run 40% last year but barely did 10% due to injury. I have a lot of data points. I don't see the average person doing even the suggested rate of 10km, 3 days per week at a 10km/hr. In fact the only regular people I see are other runners. This is of course anecdotal. But the figures for the weight of Australians isn't. [3]

A more interesting experimental question would be, "what is the minimum speed/distance you need to do per day to get the maximum health benifit?". At the moment it's 10K steps per day. Hence the reason I'm so active. One alternative to running I suggest is climbing steep terrain ~ http://www.flickr.com/photos/bootload/sets/72157623445003205... You can exert yourself just as much in a much shorter distance and time.

[0] http://www.britannica.com/EBchecked/topic/624659/Vegetius

[1] http://www.garyb.0catch.com/march8_suppl/march_suppl.html

[2] http://www.ibiblio.org/pub/academic/history/marshall/militar...

[3] "Overweight and obesity from childhood to adulthood: a follow-up of participants in the 1985 Australian Schools Health and Fitness Survey", pdf ~ http://www.mja.com.au/public/issues/186_09_070507/ven11183_f...