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)%0D%0AResponses%0D%0A%0D%0A12 hours%0D%0AStart Fraction 1 over 2 End Fraction hours%0D%0A%0D%0A112%0D%0A1 Start Fraction 1 over 2 End Fraction%0D%0A%0D%0A23 hours%0D%0AStart Fraction 2 over 3 End Fraction hours%0D%0A%0D%0A1 hour
To find the total time it will take Iris to complete the entire floor, we can use the equation:
(time to complete 23 of the floor) / (23 of the floor completed in 1/3 of an hour) = (total time) / (1)
Let's solve this equation:
(total time) / (1) = (13/23) / (1/3)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(total time) = (13/23) * (3/1)
(total time) = 39/23
Therefore, it will take Iris 39/23 of an hour to complete the entire floor.
To find out how long it will take Iris to complete the entire floor, we need to find the time it takes her to complete 1 floor unit (in this case, 23).
We know that Iris completes 23 units of the floor in 1/3 of an hour.
To find out the time it takes her to complete 1 unit of the floor, we divide the time it takes to complete 23 units by 23:
(1/3) hour ÷ 23 = 1/69 hour per unit.
Therefore, it will take Iris 1/69 hour to complete 1 floor unit.
Since she has to complete the entire floor, which consists of 23 units, we can multiply the time it takes for 1 unit by 23:
(1/69) hour × 23 = 23/69 hour
So, it will take Iris 23/69 hour to complete the entire floor.
To find out how long it will take Iris to complete the entire floor, we need to use a proportion and solve for the unknown time.
Let's set up the proportion:
23 parts of the floor / 13 parts of an hour = 1 whole floor / x hours
To solve for x, we can cross-multiply:
23x = 13 * 1
23x = 13
Now, divide both sides by 23 to isolate x:
x = 13 / 23
To simplify the fraction, we can't reduce it any further, so the final answer is:
x = 13/23 hours
Therefore, it will take Iris approximately 13/23 hours to complete the entire floor.