There are several factors that can cause hair to grow at an abnormal rate or even induce new hair growth, such as taking certain medications, fluctuations in your hormone levels, genetic traits, to name a few.
While it is impossible for me to predict the amount of time it will take for you to reach your goals, there is published documentation that describes the average experience.
This first chart describes what typical percentage of hair is actively growing (in the “anagen stage”) as well as the typical percentage of hairs in the resting phase (or “telogen stage”).
Here is another chart that describes the time an average person requires to clear a particular area:
Please note that the amount of time required to reach your goals is highly dependent on your commitment to the process: the number of times you come per week and the regularity of your appointments.