Iris is asked to sweep the gymnasium floor after a basketball game. This requires her to push a sweeper from one end of the gym to the other and repeating the pattern until she has covered the entire floor. She completes 23

Question

of the floor in 13
of an hour. At this rate, how long will it take her to complete the entire floor?(1 point)
Responses

1 hour
1 hour

23
hours
Start Fraction 2 over 3 End Fraction hours

112
1 Start Fraction 1 over 2 End Fraction

12
hours

Answer 1

To determine how long it will take Iris to sweep the entire gymnasium floor, first, we need to find the rate at which she is working.

Iris sweeps \(\frac{2}{3}\) of the floor in \(\frac{1}{3}\) of an hour. To understand how long it would take her to sweep the entire floor, we can set up a proportion.

If she completes \(\frac{2}{3}\) of the floor in \(\frac{1}{3}\) of an hour, we can find the time it takes to complete \(1\) (the whole floor) by using the following calculation:

1. Find out how many of her \(\frac{2}{3}\) portions fit into 1 full floor: \[ \text{Number of portions} = \frac{1}{\frac{2}{3}} = \frac{3}{2} = 1.5 \]

2. Since \(\frac{2}{3}\) of the floor takes \(\frac{1}{3}\) of an hour, we multiply this by 1.5: \[ \text{Total time} = 1.5 \times \frac{1}{3} \text{ hour} = \frac{1.5}{3} = \frac{1}{2} \text{ hour} \]

So to sweep the entire floor, it would take her 1 hour.

Therefore, the correct response is: 1 hour