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:

\[ \frac{2}{3} \text{ of the floor } \longrightarrow \frac{1}{3} \text{ of an hour} \] \[ 1 \text{ of the floor } \longrightarrow x \text{ hours} \]

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.