Surely you just charge your hourly rate. Thats what i do and then never get stung. I get paid for the amount of time i am there.
I'd never let anyone know my hourly rate.
Especially not a client.
Piece work, everybody knows where they stand then.
If after an hour or so you're not where you want to be either suck it up and treat it as a learning curve or renegotiate.
JMO