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?
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.
To find out how long it will take Iris to complete the entire floor, we can set up a proportion using the relationship between the proportion of the floor completed and the time taken.
Let's use the following variables:
- f: fraction of the floor completed
- t: time taken to complete the floor
According to the given information, Iris completes 2/3 of the floor in 1/3 of an hour. So, we can write:
(2/3)/(1/3) = f/t
To simplify, we can first divide the numerator and the denominator on the left side:
2/3 * 3/1 = f/t
Multiplying, we get:
6/3 = f/t
Reducing the fraction on the left side, we have:
2 = f/t
Now we can solve for t by isolating it:
t = f/2
Since f represents the entire floor, the fraction of the floor completed is 1. Therefore,
t = 1/2
So, it will take Iris 1/2 hour to complete the entire floor.
To find out how long it will take Iris to complete the entire floor, we can use the concept of ratio and proportion.
We know that Iris completes 2/3 of the floor in 1/3 of an hour. Let's represent the time it takes to complete the entire floor as 'x' hours.
So, the ratio of the portion of the floor completed to the time taken is constant. We can write this as:
(2/3) / (1/3) = 1 / x
To simplify, we can invert and multiply:
(2/3) * (3/1) = 1 / x
2 = 1 / x
Now, to find 'x', we need to isolate it:
2x = 1
Divide both sides of the equation by 2:
x = 1/2
Therefore, it will take Iris 1/2 of an hour to complete the entire floor.