How can I help my mother who believes she is constantly dirty?

A fellow caregiver asked...

My mother is 86 and in good health. She's living on her own, though I recently moved in across the street. Does anyone have any experience with their aging parent suddenly thinking they are dirty all the time? My mom thinks her skin is dirty, to the point where she showers for 45 minutes at a time every day. Any suggestions? She still insists that she must be dirty, that the water turns black. Thank you.