1. **Problem statement:** Two persons can fit a window together in 3 days. One person falls ill, so we want to find how many days it will take for the remaining person to fit the window alone. 2. **Formula and concept:** When two people work together, their combined work rate is the sum of their individual work rates. Work rate is defined as the fraction of the job done per day. 3. **Calculate combined work rate:** If two persons complete the job in 3 days, their combined work rate is: $$\text{Rate}_{combined} = \frac{1}{3}$$ 4. **Assuming both persons have the same work rate:** Let the work rate of one person be $r$. Then: $$2r = \frac{1}{3}$$ 5. **Solve for one person's work rate:** $$r = \frac{1}{6}$$ 6. **Calculate time for one person to complete the job:** Time is the reciprocal of work rate: $$\text{Time} = \frac{1}{r} = 6$$ 7. **Answer:** It will take the single person 6 days to fit the window alone.