For me, 15 hours is far, far too long for me to be an adequate caregiver. Heck, my kids are barely up for 15 hours (and they are my own and I love them). I couldn't handle it with another one.
In addition, how old is this child? Being out of the house from 5am to almost 9pm is too long for a child IMO. I think a nanny in the child's own home would be a better choice for this mom.