To find out how long it will take Iris to sweep the entire gym floor, we start with the information given:
Iris completes \( \frac{2}{3} \) of the floor in \( \frac{1}{3} \) of an hour.
To find out how long it takes her to complete the entire floor, we can set up a proportion.
If \( \frac{2}{3} \) of the floor takes \( \frac{1}{3} \) of an hour, then for 1 whole floor (1), we can find the total time \( x \):
\[ \frac{2}{3} \ \text{floor} \ \to \ \frac{1}{3} \ \text{hour} \] \[ 1 \ \text{floor} \ \to \ x \ \text{hours} \]
We can set up the equation:
\[ \frac{2}{3} \ \text{floor} = \frac{1}{3} \ \text{hour} \] \[ 1 \ \text{floor} = x \ \text{hours} \] \[ \frac{2}{3} \div \frac{1}{3} = 1 \div x \]
Calculating \( \frac{2/3}{1/3} \):
\[ \frac{2}{3} \div \frac{1}{3} = \frac{2}{3} \times \frac{3}{1} = 2 \]
So, we have:
\[ 2 = \frac{1}{x} \]
Flipping this gives:
\[ x = \frac{1}{2} \]
So, it will take Iris \( \frac{1}{2} \) hour to complete the entire floor.
The correct response is:
Start Fraction 1 over 2 End Fraction hours.
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