I agree with all of that, except for making it a reasonable rate. Go up to the edge of reasonable, then bump it up by $15/h.
If you are contracting in a situation like this a reasonable rate could mean $250-$1000 an hour. Really depends on what kind of money your currently make.
A better approach in the case would be to offer to investigate, and provide a flat rate. You can charge $3000 flat fee, and you may solve it in 1.5 hrs.