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
To determine how long it will take Iris to complete the entire floor, we can analyze the information given.
We know that Iris completed 2/3 of the floor in 1/3 of an hour. This means that in 1/3 of an hour, she completed 2/3 of the floor.
To find out how long it will take Iris to complete the entire floor (1 whole floor), we need to set up a proportion.
Let's set up the proportion as follows:
(2/3) floor / (1/3) hour = 1 floor / x hours
To solve for x (the time it will take Iris to complete the entire floor), we can cross multiply:
(2/3) floor * x hours = (1/3) hour * 1 floor
Now, we can simplify the equation by canceling out the units:
2x / 3 = 1 / 3
To isolate x, we can multiply both sides of the equation by the reciprocal of 2/3:
(2x / 3) * (3 / 2) = (1 / 3) * (3 / 2)
Simplifying further:
2x / 2 = 1 / 2
x = 1 / 2
Therefore, it will take Iris 1/2 hour (or 30 minutes) to complete the entire floor.
If Iris completes 2/3 of the floor in 1/3 of an hour, it means she covers 2/3 / (1/3) = 2/3 * 3/1 = <<2/3/(1/3)=2>>2 times the length of the gym in one hour.
Since she needs to cover the entire floor, which is 3 times the length of the gym, it will take her 3/2 * 1 = <<3/2*1=1.5>>1.5 hours. Answer: \boxed{1.5}.
To find out how long it will take Iris to complete the entire floor, we need to determine the ratio between the distance she has covered and the time it took her. Then we can use that ratio to calculate the time required to complete the entire floor.
Given that Iris completes 2/3 of the floor in 1/3 of an hour, we can calculate the ratio as follows:
Distance covered = 2/3 of the floor
Time taken = 1/3 of an hour
Now, we can set up a proportion to find the time required to complete the entire floor:
2/3 of the floor / 1/3 of an hour = total floor / x hours
To solve for x, we can cross-multiply:
(2/3) / (1/3) = total floor / x
Simplifying the left side of the equation:
(2/3) * (3/1) = (total floor) / x
Multiplying the fractions:
(2 * 3) / 1 = (total floor) / x
6 = (total floor) / x
Now, we can isolate x by multiplying both sides of the equation by x:
6x = total floor
Dividing both sides of the equation by 6:
x = (total floor) / 6
Therefore, it will take Iris (total floor) / 6 hours to complete the entire floor.