Need some advice on working out the team velocity for a sprint.

Our team normally consists of about 4 developers and 2 testers. The scrum master insists that every team member should contribute equally to the velocity calculation i.e. we should not distinguish between developers and testers when working out how much we can do in a sprint. The is correct according to Scrum, but here's the problem.

Despite suggestions to the contrary, testers never help with non-test tasks and developers never help with non-dev tasks, so we are not cross functional team members at all. Also, despite various suggestions, testers normally spend the first few days of each sprint waiting for something to test.

The end result is that typically we take on far more dev work than we actually have capacity for in the sprint. For example, the developers might contribute 20 days to the velocity calculation and the testers 10 days. If you add up the tasks after sprint planning though, dev tasks add up to 25 days and test tasks add up to 5 days.

How do you guys deal with this sort of situation?