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

Question

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 $\frac{2}{3}$ of the gymnasium floor in $\frac{1}{3}$ of an hour. To find out how long it will take her to complete the entire floor, we can set up a proportion.

If $\frac{2}{3}$ of the floor takes $\frac{1}{3}$ of an hour, we can find the time to complete $1$ whole floor by scaling.

Let $x$ be the time (in hours) it takes her to complete the entire floor. Since $\frac{2}{3}$ of the floor takes $\frac{1}{3}$ of an hour, we can set up the equation:

$$\frac{2}{3}\text{ of the floor }⟶\frac{1}{3}\text{ of an hour}$$ $$1\text{ of the floor }⟶x\text{ hours}$$

Using cross-multiplication, we can write:

$$\frac{2}{3}\times x=\frac{1}{3}$$

Now, we can solve for $x$:

1. Multiply both sides by 3 to eliminate the fraction:

$$2x=1$$

2. Divide both sides by 2:

$$x=\frac{1}{2}$$

Therefore, it will take Iris $\frac{1}{2}$ hour to complete the entire floor.

In terms of minutes, $\frac{1}{2}$ hour is equal to 30 minutes.

Thus, the answer is:

It will take Iris 30 minutes to complete the entire floor.