Yeah, you can charge whatever the market will bear. I get $40-$50. The interesting thing is, all of the kids I tutor are public school students and the parents have told me they rationalize the expense as being part of their education budget, which comes out far below their private school counterparts.
The interesting thing is, it's the low-income families who have been more adamant about getting their kids private tutoring, and have been better about sticking to a schedule. You would be surprised at how many parents with kids failing three subjects feel the need to prioritize soccer or baseball over schoolwork.
Of course, if you find out the family lives in a housing project or something, I would lower the rates a lot out of simple altruism. That has been the case with my clients at least a couple of times.