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?
Options:
2/3 hours
1/2 hours
1 1/2 hours
1 hour
To find the amount of time it will take Iris to complete the entire floor, we can set up a proportion.
If Iris completes 2/3 of the floor in 1/3 of an hour, we can set up the 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
Simplifying, we have:
2x/3 = 1/3
Cross multiplying again, we have:
2x = 1
Dividing both sides by 2, we have:
x = 1/2
Therefore, it will take Iris 1/2 hour to complete the entire floor.
Answer: 1/2 hours
To find out how long it will take Iris to complete the entire floor, we need to determine the proportion of the floor she completes in one hour.
Since Iris completes 2/3 of the floor in 1/3 of an hour, we can say that she completes (2/3) / (1/3) = 2/1 = 2 times the entire floor in 1 hour.
Thus, it will take Iris 1/2 hours to complete the entire floor.
Therefore, the correct option is 1/2 hours.
To solve this problem, we can use the concept of proportions. Let's start by setting up a proportion:
The amount of floor completed is directly proportional to the time taken.
Let's assume it will take "x" amount of time for Iris to complete the entire floor. According to the information given, she completed 2/3 of the floor in 1/3 of an hour. Therefore, we can set up the proportion:
(2/3) / (1/3) = 1 / x
To solve this proportion, we can cross multiply:
(2/3) * x = 1 * (1/3)
2x/3 = 1/3
Now, we can solve for x by multiplying both sides by 3:
2x = 1
Dividing both sides by 2 gives us:
x = 1/2
Therefore, it will take Iris 1/2 hour to complete the entire floor.
Thus, the correct answer is:
1/2 hours