OK, so, first things first, I realize that people like posting in the sections towards the top because thats where the most readers are, but I moved this thread to the appropriate section. Please try to find the most appropriate section for your post before putting it up.
In response to your question: it depends dramatically on the gym that you go to. Most gyms have a minimum of one year before getting a bluebelt, so that is fairly consistent. The difference is that some gyms also require results in competition which can make that process take much longer. If all they require is a test every three months for about a year or so, then that is how long it will take for you to earn your bluebelt.
If, like the place I currently train at in the Bay Area, advancement past white belt is based on your ability to place in a tournament setting, then it can take two or three years depending on how much you compete and how fast you take to competition.
If you are training four or five times a week, then you should be good in competition, and improve in skills fairly quickly. However, I think that the focus on improvement is more relevant than the improvement in rank. There are white belts who can submit bluebelts and there are bluebelts who shouldn't be bluebelts. You may want to be a bluebelt for the prestige, but (as hard as this is in a hierarchal training environment) try not to think about that. Learn the techniques, and try to apply them in sparring. If you are successful, then that's what the focus should be.
Worry about being good at jiu-jitsu. The rank comes later.
Sig by Toxic
Barnett - Toquinho -Werdum - "Nurmie"
Z. Gurgel - Morango - Rocha - Tiequan