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
cover the entire floor?
If Iris is able to complete 2/3 of the floor in 1/3 of an hour, we can conclude that it takes her 1/3 of an hour to cover 2/3 of the floor.
To find out how long it will take her to cover the entire floor, we need to determine the ratio of time to the ratio of floor covered.
The ratio of time is 1/3 (hour) and the ratio of floor covered is 2/3 (of the entire floor).
If we set up a proportion, we get:
1/3 hour / 2/3 floor = x hour/ 1 floor
Cross-multiplying, we have:
(1/3)(1 floor) = (2/3)(x hour)
1/3 = (2/3)(x)
1 = 2x/3
Multiplying both sides by 3, we get:
3 = 2x
Dividing both sides by 2, we get:
3/2 = x
Thus, it will take Iris 3/2 of an hour (or 1.5 hours) to cover the entire gymnasium floor.