Nobody can answer your question. It depends on how fast you adjust to altitude, how much pain you're willing to endure, what the weather looks like, etc. How much time you take off also depends on how much you want to reach the top. The longer you stay, the better your chances.
Since time off during the AK climbing season is hard for me, I have thought about the shortest trip I would do. I wouldn't consider anything less than 2 weeks on the mountain, but I live at 9000' and train between 9000 and 14000 feet (usually between 10 and 13k). Even if I could get up it faster, I wouldn't allow less time since the weather is unpredictable far enough out to deal with permits. (Personally, I would rather go for 3 weeks and stay off the west butt).