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?

Answer 1

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

2/3 (fraction of the floor she has completed) : 1/3 (time it took her to complete 2/3 of the floor) = 1 (whole floor) : x (time to complete the entire floor)

Using cross-multiplication, we get:

2/3 * x = 1/3 * 1

Simplifying the right side, we have:

2/3 * x = 1/3

To isolate x, we divide both sides of the equation by 2/3:

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

Simplifying the right side by multiplying the numerator by the reciprocal of the denominator, we get:

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

x = 1/2

Therefore, it will take Iris 1/2 of an hour to complete the entire floor.