I charge $32 for a 10 hour day (7-5) and so I would charge at least $40 for 11 hours.
I, however am very strict on not accepting kids after 5pm, NO MATTER WHAT.
This is my family's time and my time to get supper ready and clean up toys, bathrooms etc.
I did it one time for a family to go on an anniversary dinner, and I told them I am charging an extra $10 per hour after 5:00pm.
Where I live, 9 hours is the norm for how long I have my kids here so I have not had many inquiries for longer days.
Feel free to give yourself a time and a half rate for more that 9 hours, and if she can find cheaper, than yes, wish her luck and say good bye