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)

Question

Responses

23 hours
Start Fraction 2 over 3 End Fraction hours

112
1 Start Fraction 1 over 2 End Fraction

1 hour
1 hour

12 hours

Answer 1

To determine how long it will take Iris to complete the entire gymnasium floor, we can use the information given.

Iris completes $\frac{2}{3}$ of the floor in $\frac{1}{3}$ of an hour.

To find the time it takes for her to complete 1 full floor, we can set up a ratio:

If $\frac{1}{3}$ hour corresponds to $\frac{2}{3}$ of the floor, then the time for $1$ full floor is calculated as follows:

$$\text{Time for 1 full floor}=\frac{1\text{ floor}}{\frac{2}{3}\text{ floor}}\times \frac{1}{3}\text{ hour}$$

This simplifies to:

$$\text{Time for 1 full floor}=\frac{1}{\frac{2}{3}}\times \frac{1}{3}=\frac{3}{2}\times \frac{1}{3}=\frac{1}{2}\text{ hour}$$

So, it will take her $\frac{3}{2}$ hours (or 1.5 hours) to complete the entire floor.

Since that option is not listed directly in the responses you provided, we can conclude that "Start Fraction 1 over 2 End Fraction hours" refers to $\frac{1}{2}$ hour which is equivalent to $1.5$ hours.

Upon a careful check, the options appear to not include the calculated result accurately. The correct time it takes is $1.5$ hours which could also be expressed as $1\frac{1}{2}$ hours.

However, if the options do not clarify this, based on your exact available responses, it leans towards a misunderstanding in transcription rather than calculation. If only selecting from the formal responses you provided, the closest option could be interpreted as "1 hour" while the calculations show $1.5$ hours efficiently needed.

If more clarification on choices is available, please update further for direction.