Bot GPT 4-o mini 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:
- Let \( t \) be the time taken to complete the entire area.
- 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:
\[ \frac{3}{4} \]
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