To find out how long it will take Iris to complete the entire floor, we can first determine her rate of work.
Iris completes \( \frac{2}{3} \) of the floor in \( \frac{1}{3} \) of an hour.
To find the time it takes to complete the whole floor, we can set up the following proportion:
If \( \frac{2}{3} \) of the floor takes \( \frac{1}{3} \) of an hour, then \( 1 \) (the entire floor) would take:
\[ \text{Time for entire floor} = \frac{1}{3} \text{ hour} \div \frac{2}{3} = \frac{1}{3} \times \frac{3}{2} = \frac{1}{2} \text{ hour} \]
Thus, it will take Iris \( \frac{1}{2} \) hour (or 30 minutes) to complete the entire floor.