Question

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) .

Answer 1

If Iris completes \( \frac{2}{3} \) of the floor in \( \frac{1}{3} \) of an hour, we can use this information to determine how long it will take her to complete the entire floor.

First, we find out how long it takes her to complete the entire floor. If \( \frac{2}{3} \) of the floor takes \( \frac{1}{3} \) of an hour, we can calculate the time for the full floor as follows:

Let \( t \) be the time in hours to complete the entire floor. We can set up the ratio:

\[ \frac{\frac{2}{3}}{t} = \frac{\frac{1}{3}}{\frac{1}{3}} \]

Simplifying this, we can cross-multiply to find:

\[ 2t = 1 \]

Thus, solving for \( t \):

\[ t = \frac{1}{2} \text{ hours} \]

In minutes, \( \frac{1}{2} \) hour is equal to \( 30 \) minutes.

Therefore, it will take Iris \( 30 \) minutes to complete the entire floor.