Iris is asked to sweep the gymnasium floor after a basketball game. This requires her to push a sweeper from one 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?
If Iris completes 2/3 of the floor in 1/3 of an hour, then she completes 1/3 * (1/3) = 1/9 of the floor in 1/3 of an hour.
If she completes 1/9 of the floor in 1/3 of an hour, then it will take her 1 / (1/9) = 9/1 = <<1/(1/9)=9>>9 hours to complete the entire floor. Answer: \boxed{9}.
If Iris completes 2/3 of the floor in 1/3 of an hour, then she completes 1/3 of the floor in 1/6 of an hour.
To calculate how long it will take her to complete the entire floor, we can set up a proportion:
(1/3 of the floor) / (1/6 of an hour) = (the entire floor) / (x hours)
To solve for x, we can cross multiply:
(1/3) / (1/6) = (the entire floor) / (x)
(1/3) * (6/1) = (the entire floor) / (x)
6/3 = (the entire floor) / (x)
2 = (the entire floor) / (x)
To find the value of x, we can divide both sides of the equation by 2:
2/2 = (the entire floor) / (x) / 2
1 = (the entire floor) / (x)
Therefore, it will take her 1 hour to complete the entire floor.
To find out how long it will take Iris to complete the entire floor, we need to determine the total time she took to complete 2/3 of the floor and then use that information to calculate the remaining time needed.
Let's start by calculating the time it took her to complete 2/3 of the floor.
We are given that she completed 2/3 of the floor in 1/3 of an hour.
So, to find the time it took her to complete the entire floor, we need to scale up the time by dividing 1/3 by 2/3.
We can do that by multiplying 1/3 by the reciprocal of 2/3, which is 3/2.
(1/3) * (3/2) = (1/3) * (3/2) = 1/2
Therefore, it took Iris 1/2 hour to complete 2/3 of the floor.
Now, we can calculate the remaining time needed to complete the entire floor.
Since she has already completed 2/3 of the floor in 1/2 hour, the remaining 1/3 of the floor will take the same amount of time.
So, it will take Iris an additional 1/2 hour to complete the remaining 1/3 of the floor.
Therefore, the total time it will take her to complete the entire floor is:
1/2 hour (for 2/3 of the floor) + 1/2 hour (for the remaining 1/3) = 1 hour.
Hence, it will take Iris 1 hour to complete the entire floor at this rate.