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?
To complete 2/3 of the floor in 1/3 of an hour, Iris completes 2/3 / 1/3 = <<2/3/1/3=2>>2 floors per hour.
Therefore, it will take her 1/2 an hour to complete 1 floor.
Thus, it will take her 1/2 * 3 = 3/2 hour to complete 3 floors. Answer: \boxed{\frac{3}{2}}.
To find out how long it will take Iris to complete the entire floor, we first need to determine the time it takes for her to complete 1/3 of the floor.
If Iris completes 2/3 of the floor in 1/3 of an hour, it means she covers 2/3 of the floor in 1/3 of the time.
To find out the time it takes for Iris to complete 1/3 of the floor, we can set up a proportion:
(2/3) floor / (1/3) hour = 1 floor / x
Simplifying the proportion, we get:
(2/3) / (1/3) = 1 / x
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(2/3) * (3/1) = 1 / x
The 3s cancel out, leaving us with:
2 = 1 / x
To solve for x, we can take the reciprocal of both sides:
1/2 = x
Therefore, it will take Iris 1/2 hour to complete 1/3 of the floor.
Since she needs to repeat the pattern until she has covered the entire floor, it will take her 3 times longer to complete the entire floor:
1/2 hour * 3 = 1 1/2 hours
Therefore, it will take Iris 1 1/2 hours to complete the entire floor.
To find out how long it will take Iris to complete the entire floor, we can set up a proportion using the information given.
We know that Iris completes 2/3 of the floor in 1/3 of an hour. Let's use "x" to represent the time it will take her to complete the entire floor.
The proportion can be set up as follows:
(2/3) / (1/3) = 1 / x
To solve for "x", we can cross multiply:
(2/3) * x = 1 * (1/3)
Next, we simplify both sides of the equation:
2x / 3 = 1/3
Now, we can multiply both sides of the equation by 3 to eliminate the fractions:
(2x / 3) * 3 = (1/3) * 3
2x = 1
Finally, we isolate "x" by dividing both sides of the equation by 2:
2x / 2 = 1 / 2
x = 1/2
Therefore, it will take Iris a total of 1/2 hour or 30 minutes to complete the entire gymnasium floor.