I (personally) think you shouldn't decrease your expected rate (if 40 is something that works for you) because you don't have enough experience. Experience is important, don't get me wrong, but they will be paying for results, so to say. And it's your portfolio that shows what you are capable of.
I'd consider the following: How long do you think it would take you to improve so you should be making $40/h? Suppose it's 6 months, will you be comfortable asking them to increase your hourly rate at this point?
If they did a search and couldn't find other candidates, that must mean you are good at what you do. Your talent has a value, and even if you haven't worked that much in the industry you must have invested time in learning your tools.
If you feel it's not fair for you to be making as much as others with more experience make, here's an idea: If something takes you 1/3 longer than others, you could use your own time to finish those projects or train to supply those areas you are not that strong in. So if something takes you 3 hours, but you are sure you had difficulties because of your lack of experience, you could absorb that last hour and charge them for two. Consider this more of a 'moral workaround' that you could use the first couple of months :)