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

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

12
hours
Start Fraction 1 over 2 End Fraction hours

1 hour
1 hour

112
1 Start Fraction 1 over 2 End Fraction

23
hours

1 answer

To determine how long it will take Iris to complete the entire floor, we first need to see how much of the floor she covers in one hour based on the information provided.

Iris completes \( \frac{23}{13} \) of the floor in one hour. To find out how long it will take her to complete the entire floor (which is 1 whole floor), we can set up a proportion:

  1. Find the rate of completion per hour:

    • If Iris completes \( \frac{23}{13} \) of the floor in 1 hour, we need to calculate how many floors she can complete in 1 hour: \[ \text{Rate} = \frac{23/13 \text{ (floors)}}{1 \text{ (hour)}} = \frac{23}{13} \text{ floors/hour} \]
  2. Determine the time to complete 1 whole floor:

    • To find out how long it takes for 1 whole floor, we find the reciprocal of her rate: \[ \text{Time to complete 1 floor} = \frac{1 \text{ floor}}{\frac{23}{13} \text{ floors/hour}} = \frac{13}{23} \text{ hours} \]

Thus, it will take Iris \( \frac{13}{23} \) hours to complete the entire floor. Since \( \frac{13}{23} \) is approximately \( 0.565 \) hours, you can convert it to a mixed number to provide clear options:

This is slightly more than half an hour, often said as:

\[ 0.565 \text{ hours} = \frac{1}{2} \text{ hours } + \text{ some minutes (about 34 minutes)} \]

Among the options given, the closest and best match is:

Start Fraction 1 over 2 End Fraction hours.