The time it takes for Alzheimer's patients to die depends on how severe the Alzheimer's disease is and what sage the person is in Alzheimer's disease.
Some Alzheimer's patients die within 5 to 10 years of diagnoses of Alzheimer's disease while some patients like my aunt lived for 20 years with Alzheimer's disease before she passed away.
So it can vary from person to person and how severe the Alzheimer's disease condition is.