Question

Charla wants to cover a certain rectangular area of her driveway with a picture using chalk. If she completes 2/3
of the area in 1/2
hour, how long will it take her to complete the entire picture? Enter your answer as a simplified fraction.

Answer 1

To determine how long it will take Charla to complete the entire picture, we can first analyze how much work she does in a given amount of time.

Charla completes \( \frac{2}{3} \) of the area in \( \frac{1}{2} \) hour.

To find out the time it takes to complete the entire area, we can set up a proportion based on the work done:

1. Let \( t \) be the time taken to complete the entire area.
2. In \( \frac{1}{2} \) hour, she completes \( \frac{2}{3} \) of the area, so we can express the total time required as:

\[
\frac{2}{3} \text{ of the area corresponds to } \frac{1}{2} \text{ hour.}
\]

If \( \frac{2}{3} \) of the work corresponds to \( \frac{1}{2} \) hour, then \( 1 \) (the entire area) corresponds to:

\[
t = \frac{1}{2} \text{ hour} \div \frac{2}{3} = \frac{1}{2} \times \frac{3}{2} = \frac{3}{4} \text{ hours.}
\]

So, it will take Charla \( \frac{3}{4} \) hours to complete the entire picture.

Therefore, the answer is:

\[
\frac{3}{4}
\]