I did this same Invitational last year when a parent asked I'd shoot photos of her son. The venue is an hour away from studio and I only charged her $75, but I was there for maybe 6 hrs....which was just long enough to shoot her son's events, which were spread out.
Having said all that...I've been asked to do this again and thinking of charging an hourly rate. I need to reply to this client ASAP, and thought she could pool with some other parents to off set her costs...I know the rate depends on region, (My wedding rate is $150/hr. after package time expires)....so I thought of asking $60-$75 per hour and they can tell me how long they want me for. Any thoughts?

