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 1/2
1 Start Fraction 1 over 2 End Fraction

2/3 hours
Start Fraction 2 over 3 End Fraction hours

1 hour
1 hour

1/2 hours

1 answer

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

If \( \frac{2}{3} \) of the floor takes \( \frac{1}{3} \) of an hour, then for the whole floor (1 full floor), we can calculate the time it takes as follows:

Let \( x \) be the time to complete the entire floor:

\[ \frac{2}{3} \text{ floor} \quad \text{takes} \quad \frac{1}{3} \text{ hour} \]

So, for 1 floor:

\[ 1 \text{ floor} \quad \text{takes} \quad x \text{ hours} \]

Using proportions, we have:

\[ \frac{2/3}{1} = \frac{1/3}{x} \]

Cross-multiplying leads to:

\[ 2x = 1 \]

Solving for \( x \):

\[ x = \frac{1}{2} \text{ hour} \]

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

So, the answer is:

1/2 hours.