Iris is asked to sweep the gymnastics 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?
Since Iris completes 2/3 of the floor in 1/3 of an hour, this means she can complete 1/3 of the floor per 1/3 hour. Therefore, she can complete the entire floor in 1 hour. Answer: \boxed{1}.
To find out how long it will take Iris to complete the entire floor, we need to compare the proportion of the floor she completed to the time it took her.
Step 1: Find the proportional relationship between the floor covered and the time taken.
Since Iris completed 2/3 of the floor in 1/3 of an hour, we have the ratio:
(2/3) floor : (1/3) hour
Step 2: Simplify the ratio.
Multiply both parts of the ratio by 3 to get rid of fractions:
(2/3) * 3 floor : (1/3) * 3 hour
2 floor : 1 hour
Step 3: Find the time it takes for Iris to complete the entire floor.
Since we have the ratio of 2 floor : 1 hour, it will take her 1 hour to complete the entire floor.
Therefore, it will take Iris 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 her rate of sweeping. We can do this by dividing the fraction of the floor she completed by the fraction of an hour she took:
Rate = Fraction of floor completed / Fraction of hour taken
From the information given, Iris completed 2/3 of the floor in 1/3 of an hour:
Rate = (2/3) / (1/3)
To divide by a fraction, we can multiply by the reciprocal of that fraction:
Rate = (2/3) * (3/1)
Simplifying, we get:
Rate = 2
So, Iris' rate of sweeping is 2/1 or simply 2.
Now, to find out how long it will take her to complete the entire floor, we need to calculate the time it will take at this rate. Let's call the time to sweep the entire floor "T" (in hours).
Rate = Distance / Time
Since Iris is sweeping the entire floor, the distance is 1 (the whole floor) and the rate is 2:
2 = 1 / T
To isolate "T", we can divide both sides of the equation by 2:
2/2 = 1/T
1 = 1/T
Now, we can see that the time it will take Iris to complete the entire floor is 1 hour.
Therefore, it will take Iris 1 hour to complete the entire floor.