I agree with Playfelt. I don't think charging by the minute would work in your favour. I would however ask if she needs their pickup time extended and charge accordingly. I do $5 per 15 mins. You didn't mention what this child is like. How old? How demanding is the child at at this point in the day? Are they easy to keep occupied with something like tv or colouring while you start your clean up and dinner? If so I would do that. I have one parent who is always picking up right at my closing time and at that point in the day, the kids are DONE and I am DONE so its a video or free play while I prep my dinner. I make a point of saying "Oh I just put a dvd on so I could make my dinner because we have soccer/karate/etc tonight." They don't seem the mind.