Gas reimbursement rate is 72.5 cents per mile.

I like to pay $50 per solo and the student gets 2 15 minute rehearsals plus performance with the pianist.

With state being so far away and this taking up their entire day - I think paying them $250 for the day plus expenses would be fair. If they're playing for more than 3 or 4 soloists - I would add another $50 per solo.

Remember that it's likely that they have private students they are going to have to reschedule lessons for. Many of these pianists teach on Saturdays.

If you're not completely set on the pianist you've been working with - you could look at trekorda depending on what area you're in. They have pianists in some areas of the state available for rehearsals at your school the week before state and they will be at the state contest playing for quite a few schools.