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 23 of the floor in 13 of an hour. At this rate, how long will it take her to complete the entire floor?(1 point)

Answer 1

To determine how long it will take Iris to complete the entire gymnasium floor, we start by finding her rate of work based on the information given.

Iris completes \(\frac{23}{13}\) of the floor in one hour. To find out how long it will take to complete all of the floor (which is considered 1 full floor), we can set up a proportion where \( t \) is the time in hours it takes to complete the entire floor:

\[ \frac{23}{13} \text{ of the floor} \text{ takes } 1 \text{ hour} \] \[ 1 \text{ of the floor takes } t \text{ hours} \]

Now we can set up the equation from the rates:

\[ \frac{23}{13} \times t = 1 \]

Now solve for \( t \):

\[ t = \frac{1}{\left(\frac{23}{13}\right)} = \frac{13}{23} \]

So, it takes \(\frac{13}{23}\) hours for her to complete the entire floor.

To convert this into a more understandable format, we can multiply it by 60 (since there are 60 minutes in an hour):

\[ \frac{13}{23} \times 60 \approx 34.13 \text{ minutes} \]

Thus, it will take Iris approximately 34.13 minutes to complete the entire floor.