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?

Question

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?

A. 1 hour
B. 1/2 hours
C. 2/3 hours
D. 1 1/2

Answer 1

To find the time it will take Iris to complete the entire floor, we can set up a proportion. Since Iris completes 2/3 of the floor in 1/3 of an hour, we can write the proportion as:

(2/3) / (1/3) = 1 / x

To solve for x, the time it will take Iris to complete the entire floor, we can cross-multiply:

(2/3) * x = (1/3) * 1

Multiplying both sides:

(2/3)x = 1/3

To isolate x, we can multiply both sides by the reciprocal of 2/3, which is 3/2:

(3/2) * (2/3)x = (3/2) * (1/3)

Simplifying:

x = 1/2

Therefore, it will take Iris 1/2 hour to complete the entire floor. The answer is B. 1/2 hours.

Answer 2

To find out how long it will take Iris to complete the entire floor, we can set up a proportion based on the information given.

We know that Iris completes 2/3 of the floor in 1/3 hour. So, if she completes 2/3 of the floor in 1/3 hour, we can set up the following proportion:

(2/3) floor / (1/3) hour = 1 floor / x hours

To solve for x, we can cross-multiply:

(2/3) * x = (1/3) * 1

2x/3 = 1/3

Multiply both sides of the equation by 3:

2x = 1

Divide both sides of the equation by 2:

x = 1/2

Therefore, it will take Iris 1/2 hour (or 30 minutes) to complete the entire floor.

The correct answer is B. 1/2 hour.

Answer 3

To solve this problem, we can use the concept of proportions. We know that Iris completes 2/3 of the floor in 1/3 of an hour.

Let's set up a proportion to find out how long it will take her to complete the entire floor:
(2/3) floor / (1/3) hour = 1 floor / x hours

To solve for x, we can cross multiply:
(2/3) * x = (1/3) * 1

To simplify, we can cancel out the common factor of 1/3:
2x = 1

Now, divide both sides of the equation by 2 to solve for x:
x = 1/2

Therefore, the correct answer is B. 1/2 hour.