Our agency often needs a Personal Care Aide to work a 24-hour shift, spending the night at a client's home. When that is needed, there is a private room that is offered for you to sleep in. Would you be willing to work a 24-hour shift if needed?

The interviewer is looking to see if you are flexible and can work 24-hour shifts if needed. They want to know if you have other obligations that would preclude you from working those shifts. If you have child care issues or something else that would interfere with working long shifts, explain what those issues are and that you need notice before accepting a 24-hour shift. The agency should have posted those requirements in the job announcement, so you should be aware of that before the interview.