As to my knowledge, from many sources (including real Wikipedia), trans-warp (or warp 10) mean the infinite speed and that someone or something is everywhere in the same time. And hard part about using trans-warp is to exactly calculate and predict, where one would actually appear. Is that true?
How can then Voyager actually travel in trans-warp? In many episodes we see animation of some sort of corridor and -- what is the most important -- we clearly see, that such travel does take some time. In the end of Dark Frontier episode, captains log says even about traveling for some time and passing few thousands light years before trans-warp coil has given up the ghost.
If speed is infinite and an object is in every place in the universe in the same time, that means (at least to me -- correct me, if I'm wrong), that time part stops playing anything in this equation. For me, traveling in trans-warp doesn't actually mean to travel as in time aspect. You are here, when you initiate trans-warp coil and then, immediately, you are there. Wherever this is.