To determine how long it will take Iris to complete the entire floor, we can use the information given about the portion of the floor she has already completed.
Iris completed \( \frac{2}{3} \) of the 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 \( \frac{1}{3} \) hours, then \( 1 \) whole floor would take \( x \) hours.
The proportion is:
\[ \frac{2/3 \text{ of the floor}}{\frac{1}{3} \text{ hours}} = \frac{1 \text{ floor}}{x \text{ hours}} \]
Cross-multiplying gives:
\[ 2/3 \cdot x = \frac{1}{3} \]
Now, solve for \( x \):
\[ x = \frac{1}{3} \div \frac{2}{3} = \frac{1}{3} \cdot \frac{3}{2} = \frac{1}{2} \]
Thus, it will take Iris \( \frac{3}{2} \) hours, or 1.5 hours, to complete the entire floor.
1 answer