Really depends on your level and how far the server is. Usually once people on a new server enter arena, it is not uncommon for the fights to take 7 turns. Once you are clearly ahead of the competition you can do it fast.

Last but not least: if nobody is in ranked mode, you will be put up against a clone (bot) of a team that earlier played in the arena, so don't be surprised if you find yourself fighting someone who is not even online.