Well I know that in the 18th Century an average pace march would be about 3-4 miles per hour, though in any kind of heat that could be deadly. Now the Romans and Greeks would be carriering alot more armour than the average 18th century soldier. But also there is the training aspect. I believe that the average Roman legionnaire was in much better physical shape and training than their pre-modern counterparts. So I think that they to could maintain probably the 3 mile per hour march pace also. So if you estimate a march time of around 10 A.M. to 6 P.M.( I do not know if these are accurate march times, I think the morning should be earlier) you get daily marches around 24 miles a day.

Okay, I have been reading a bit more on the internet, This is from wikipedia:

Quote:
Vegetius, the author of the only surviving treatise on the Roman Empire's military, De Re Militari, recognized the importance of "constant practice of marching quick and together. Nor is anything of more consequence either on the march or in the line than that they should keep their ranks with the greatest exactness. For troops who march in an irregular and disorderly manner are always in great danger of being defeated. They should march with the common military step twenty miles in five summer-hours, and with the full step, which is quicker, twenty-four miles in the same number of hours. If they exceed this pace, they no longer march but run, and no certain rate can be assigned."
http://en.wikipedia.org/wiki/Military_step

So my first estimate was fairly close. The extraordinary thing about this is that they are marching at 5 miles per hour for 5 hours. This is fairly amazing, it is no wonder the Roman armies were so victorious, they could move so fast. I am sure most 18th and 19th commanders would be absolutely thrilled to have their troops move that fast. The only way most commanders could achieve such speed would be through a forced march.

I am pretty sure that Tactius also wrote about this, but I cant seem to be bothered to search the pages for that right now.