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 2/3 of the floor in 1/3 of an hour. At this rate, how long will it take her to complete the entire floor?(1 point) Responses 1 hour 1 hour 1/2 hours Start Fraction 1 over 2 End Fraction hours 1 1/2 1 Start Fraction 1 over 2 End Fraction 2/3 hours

Answer 1

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

Given that she completes \( \frac{2}{3} \) of the floor in \( \frac{1}{3} \) of an hour, we can set up a proportion to find out how long it will take to complete the entire floor.

1. First, we find the rate at which she works:

   • In \( \frac{1}{3} \) of an hour, she completes \( \frac{2}{3} \) of the floor.
   • Therefore, in 1 hour, she would complete: \[ \text{Total floor completed in 1 hour} = \frac{2}{3} \div \frac{1}{3} = 2 \text{ floors} \]

2. Now we can find out how long it would take for her to complete 1 floor:

   • If she can complete 2 floors in 1 hour, it would take her: \[ \text{Time to complete 1 floor} = \frac{1 \text{ hour}}{2} = \frac{1}{2} \text{ hour} \]

Thus, it will take Iris \( \frac{1}{2} \) hour to complete the entire floor.

The correct response is \( \frac{1}{2} \) hour (or 1/2 hours).