To determine how long it will take Iris to complete the entire floor, we first need to establish her rate of work based on the information provided.
Iris completes \( \frac{2}{3} \) of the floor in \( \frac{1}{3} \) of an hour (since she completed 23% of the floor in 13 minutes, and 13 minutes is approximately \( \frac{1}{3} \) of an hour).
To find her rate per hour, we can use the following formula:
\[ \text{Rate} = \frac{\text{Work Done}}{\text{Time}} = \frac{\frac{2}{3}}{\frac{1}{3}} = 2 \text{ (floors per hour)} \]
This means she can complete \( 2 \) of the floor in \( 1 \) hour.
Now, if she can complete \( 2 \) of the floor in \( 1 \) hour, we can figure out how long it will take her to complete \( 1 \) full gymnasium floor:
\[ \text{Time to complete 1 floor} = \frac{1 \text{ floor}}{2 \text{ floors/hour}} = \frac{1}{2} \text{ hour} \]
So the answer is: 1 Start Fraction 1 over 2 End Fraction hour (or 0.5 hours).