Unfortunately this is effected by many factors and as such there is no simple answer; some of the things to keep in mind are:

1. What is the size of is the database?
2. How many customizations are there?
3. What does the old infrastructure look like?
4. What does the new infrastructure look like?
5. Which patch level of V11 are they currently on?

Usually planning and timing an initial dry-run upgrade will give you a good idea of the time required to perform the final production upgrade. 

As REGARD HULSBOS said, it is difficult to give an estimation without context.

1. Installation af the new infrastructure : 1 month (define servers, ect.)
2. Make the migration (transform table and data): 1-2 weeks of process
3. Debugg and redevelop some customization : 1-2 weeks
4. Tests user's and/or automation of testinf with ATP : 1 month
5. Do corrections, and tests again
6. Plan and switch : 1-2 weeks

But the main variable for a migration is the part 4, testing, testing and testing

Approximately (from my experience) and with XTech upgrade tool : x-techarts.com/.../

1. If you have not a lot personalization and every body are available to set up the new a infrastructure : 2-4 months
2. If you have some personalization and every body are available to set up the new a infrastructure : 3-6 months because you have to test some features with your customization and mobilize operationnal staff
3. If you have a lot personnalization, you have to list all your developpement and plan operationnal staff to test very seriuosly your solution. 5+ months

With XTech upgrade tool, the size of the data base is not a big deal. But without XTech tool, you have to estimate the migration of data and it is not the same project.