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

Answer 1

To determine how long it will take Iris to complete the entire floor, we first need to find her rate of sweeping.

Iris sweeps \( \frac{23}{13} \) of the floor in one hour.

To find out how long it will take her to sweep the entire floor, we'll set up a proportion:

If \( \frac{23}{13} \) of the floor takes \( 1 \) hour, then \( 1 \) whole floor would take \( \frac{1 \text{ hour}}{\frac{23}{13}} \).

This can be calculated as follows:

\[ \text{Time to complete 1 floor} = \frac{1}{\frac{23}{13}} = \frac{13}{23} \text{ hours} \]

Next, let's convert \( \frac{13}{23} \) hours to a more usable format.

To convert it to minutes, multiply by 60:

\[ \frac{13}{23} \text{ hours} \times 60 \text{ minutes/hour} \approx 33.91 \text{ minutes} \]

So it will take Iris approximately 33.91 minutes (or about 34 minutes) to sweep the entire gymnasium floor.