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)
Responses

1/2 hours
Start Fraction 1 over 2 End Fraction hours

1 hour
1 hour

1 1/2
1 Start Fraction 1 over 2 End Fraction

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

1 answer

Iris completes \( \frac{2}{3} \) of the floor in \( \frac{1}{3} \) of an hour. We can find out how long it takes her to complete the entire floor by setting up the following proportion.

If \( \frac{2}{3} \) of the floor takes \( \frac{1}{3} \) of an hour, then to find the time \( t \) to complete \( 1 \) whole floor, we can set up the equation:

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

Calculating the left side:

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

This means that completing \( 2/3 \) of the floor takes \( \frac{1}{3} \) of an hour, and the time for a whole floor is \( 2 \times \frac{1}{3} \).

Now, calculating that gives:

\[ t = 2 \times \frac{1}{3} = \frac{2}{3} \text{ hours} + \frac{2}{3} \text{ hours} = 1 \text{ hour} \]

Therefore, it will take Iris \( 1 \) hour to complete the entire floor.

So the answer is:

1 hour