I may come off as chintzy, but I used to do these jobs a LOT when I was a kid. In this situation, I think something like $8/visit is appropriate, because when a young teen is a mother's helper for one kid, I think that is about what they'd get paid per hour at that age and with that experience (i.e. working under supervision). From what you're describing, she'll be there for much less than an hour, but you should round up to a full hour for the visit because of the time it'll take to get there and back, etc.. If you're asking her to play with the cats or engage them at all, or serve any wet food or simple meds, then you should up it to $10-$14 or so a visit depending on what you're asking.
I would tell the kid she's getting $8 a day, and then, when you get home, if everything looks good, give her a flat $75-$80 depending on how good everything looks. Also, bring her home a small souvenir. You aren't trying to short the kid--you want her to work out in the future and you want to have a good relationship with her. You want her to know that you value her time, but you don't want her to feel like she is owed an inflated amount for doing a very simple job. (That way, in the future, if one of your cats DOES need more careful attention or special food, you won't need to break the bank to pay her to do substantially more work--you'll simply give her the $12-$15 or so a visit that would be customary for that nature of a visit. OR you'd hire a professional, if the circumstances required it. As a cat owner with 2 very high needs cats, we wouldn't be able to rely on a neighborhood teen, so I hope you protective pet owners out there understand me.)
Don't forget--this is really good experience for the girl, as well, and you can be generous with her in recommending her to your friends and telling her that she can give your number as a reference for others!!!
Oh--and an edit-- If she already has a going per-visit rate (i.e. if others have already paid her a certain amount for similar services), then it's only appropriate to pay her rate. That doesn't mean you need to go prompting her to tell you what she gets paid--even at that age I understood that I had some clients that were wealthier than others and I didn't expect everyone to pay me the same amount. But if she comes forward and suggests that her services are already worth a certain amount, and the amount is reasonable, then you should pay it.