I wouldn't take the 12 hour day. It's hard on the kid, and it's hard on you. I've done it and I had to terminate, it was just too much.
If I was in a financial position where I had to, then I would charge an extra $5.00 per half hour outside of my normal hours. So, in your case... an extra 20 bucks. Ya, I might do 12 hours for 60 a day... however, I doubt anyone would pay it.