There are several answers to that question.
If you mean calender time:
The recommend schedule is 8 weeks of on-line study, then an additional 4 weeks of reviewing the material, taking other practice tests and learning a "memory dump." 12 weeks total from start to finish.
There are people that do it much faster. Some have completed the on-line class in 3 or 4 weeks! And, there are people that take the course but never take the exam (I don't get it). There was one woman that took this course for 3 years before she sat for her exam and passed!
We don't believe in "fast learning" being good learning. It takes time to absorb the material and feel comfortable with it when you sit at the exam terminal.
Bottom line: Its up to you!
If you mean hours / week:
It should take you about 3 hours to read the lecture and the PMBOK guide, about 1 hour answering and posting messages and about 2 hours taking practice quizzes. Approximate total per week 6 hours. Again, you could spend more time. you could re-take quizzes, you could re-read the guide...
A good estimate would be 6 to 10 hours a week.