Let's use some math to figure it out!
Right now (Jan 1, 2015), there are 926 math exercises on Khan and 536 of them are for grades K-8. So let's assume we're talking about the remaining 390 exercises, Algebra through Integral Calculus.
If you're a fantastic math PhD, then it's just a matter of answering one or two questions for each one (I think Khan gives you more credit towards mastery the faster you answer questions, at least at first). Averaging two questions per topic and taking one minute per question, that's 780 minutes and you're done in 13 hours.
If you're a brilliant elementary student who has just finished all the K-8 work but hasn't learned anything more yet, then you'll need to watch videos for each topic and work on the exercises. Maybe it would take 10 minutes for the video, 15 problems for each skill, and 1 minutes per problem in Algebra -- but it's going to slow down a lot as you get to Trigonometry and Calculus. By the time you finish, you might be watching 30 minutes of video and doing 30 problems that take 5 minutes each (and I'm unconvinced that Khan Academy is going to be able to *educate* anyone -- I think you'll still need to find other resources to fill in the blanks that the videos and exercises leave in your understanding -- this is why you'll always want to use Khan *and* an actual teacher). So let's say the average time is 20 minutes of video, and 100 minutes of exercise work, times 390, which is is 46,800, or 780 hours. An hour a day, 180 days a year, for a little more than four years -- basically, as all your friends are finishing high school.
If you're an average student who's just really determined to do it? Maybe at first it's 20 minutes for each video (watching them twice), 30 problems for each skill and 3 minutes per problem. But later on, I suspect it will become really difficult to get through the exercises with just Khan. This assumes you're *capable* of learning Integral Calculus (and all the topics that precede it). It's pretty complicated stuff, but I actually think that most people are capable of it, if sufficiently motivated. So the later topics might take an average student 30 minutes on the video, another hour researching topics elsewhere (or discussing with other teachers, tutors, or students), and 50 problems that take 5-10 minutes each, totalling 500 minutes or so per skill? So maybe an average of 300 minutes per skill, across all 390 skills -- that's 1950 hours, or 11+ years of work (at 180 hr/yr). You'd probably finish more slowly than your fellow students that went to high school and took 8 semesters of math in college.
It depends *SO* heavily upon your level of determination. Your natural mathematical ability (and your math education up to this point) matters too, but the effort you're willing to spend on the task is the single most important thing. How do you react when you get stuck in school? Do you get frustrated and give up, or do you grit your teeth and say "I will find a way to understand this!" If you're going to get through Khan, you need to be the latter type . . .
Good luck to you! And if you need a Coach on Khan, I'd be happy to volunteer (I already have 350+ students).
