I think you need to call around and ask what child care centers are charging for a full day/full week. Then do a reasonable portion of that.
For example:
Say a child care center charges 100 per week for a child that is there a normal day, 9-10 hours. 10 hours per day at 5 days they are getting $2.00 per hour. For that $2.00 per hour they are paying for at least one full meal and at least one snack and probably two snacks. If they are charging much more for the age child you would be caring for then you can adjust the math a bit. I know some centers charge almost $200 per week for an infant. But still, that would only be about $4.00 per hour.
You would be in their home using their food. You would be giving individual care. There are definantly pro's for that service that could justify charging more per hour.
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Yes, most children are in child care at LEAST 9 hours per day and the average is right at 10 hours per day. Say mom and dad work 8-5. That child is there at least half an hour before and a half hour after the parents have to be at work. That means 7:30 to 5:30 minimum. Often traffic takes up to a half hour more so they are dropped off even earlier and picked up later making an even longer day for the kiddo.