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)
Responses
112
1 Start Fraction 1 over 2 End Fraction
23 hours
Start Fraction 2 over 3 End Fraction hours
1 hour
1 hour
12 hours
To find the time it will take Iris to complete the entire floor, we can set up a proportion.
We know that Iris completed 23 of the floor in 1/3 of an hour.
Let x represent the time in hours it will take her to complete the entire floor.
So the proportion is:
23/1 = x/(1/3)
To solve for x, we can cross multiply and simplify:
23 * 1/3 = x * 1
23/3 = x
Therefore, it will take Iris 23/3 hours to complete the entire floor.
This is equivalent to 7 and 2/3 hours, or approximately 7.67 hours.
To find out how long it will take Iris to complete the entire floor, we need to determine the fraction of the floor she can sweep in one hour.
We know that she completes 23 of the floor in 13 of an hour. To find out the fraction of the floor she completes in one hour, we multiply this fraction by the reciprocal of 13. Reciprocal means flipping the fraction upside down, so the reciprocal of 13 is 1/13.
23/13 * 1/13 = 23/169
So, Iris can complete 23/169 of the floor in one hour.
To find out how long it will take her to complete the entire floor, we divide 1 (representing the entire floor) by the fraction of the floor she can complete in one hour.
1 / (23/169) = 169/23
So, it will take Iris 169/23 hours to complete the entire floor.
Simplifying the fraction 169/23, we get:
7 hours and 4/23 hours.
So, the answer is approximately 7 hours and 4/23 hours.
To find out how long it will take Iris to complete the entire floor, we can use the information that she completes 23 of the floor in 13 of an hour.
To calculate the rate at which she completes the floor, we can divide the floor completed (23) by the time taken (13):
Floor completed / Time taken = Rate
23 / 13 = 1.7692
So, Iris completes the floor at a rate of approximately 1.7692 units per hour.
To find out how long it will take her to complete the entire floor, we can set up a proportion:
Partial floor completed / Time taken = Entire floor / Unknown time
Using the rate we found (1.7692 units per hour), we know that 23 units of the floor were completed in 13 of an hour. So, we can set up the proportion:
23 / 13 = Entire floor / Unknown time
Now, we can solve for the unknown time. Cross-multiplying, we get:
23 * Unknown time = 13 * Entire floor
Unknown time = (13 * Entire floor) / 23
Given that 1 unit of the floor takes 1 hour to complete, we can substitute Entire floor with 1:
Unknown time = (13 * 1) / 23
Unknown time = 13 / 23
Therefore, Iris will take approximately 0.5652 hours to complete the entire floor.
But since the answer choices are given in whole numbers, we can convert this to minutes:
0.5652 hours * 60 minutes/hour = 33.91 minutes
Rounding to the nearest whole number, Iris will take approximately 34 minutes to complete the entire floor.
Therefore, the correct answer is: 34 minutes.