To find out how long it will take Iris to complete the entire floor, we first need to determine her rate of work.
Iris sweeps 23 of the floor in \( \frac{1}{3} \) of an hour. To find how long it takes her to complete 1 entire floor, we can set up a proportion.
If \( \frac{1}{3} \) hour is for 23 of the floor, then for the entire floor:
\[ \text{Time for 1 floor} = \frac{1}{3} \text{ hour} \div \frac{23}{1} = \frac{1}{3} \cdot \frac{1}{23} = \frac{1}{69} \text{ hour per unit} \]
Now to compute the time for the entire floor:
\[ \text{Time for 1 floor} = \left( \frac{1}{69} \text{ hour/unit} \right)^{-1} = 69 \text{ units} \] So, we just calculate that total time spent on one full floor:
\[ \text{Total time} = \text{Time for 1 floor} * 23 \]
From the previous calculation, it takes her \( \frac{1}{3} \) hours to do 23. Thus to find the time to do 1 floor:
\[ \text{Time for 1 floor} = 69 \cdot (1/3) \text{ hour} = 1 hour \]
Thus from the choices provided:
- A is 23 hours
- B is \( \frac{2}{3} \) hours
- C is \( 1\frac{1}{2} \) hours
- D is 1 hour
- E is 12 hours
The correct answer is D: 1 hour.