To find out how long it will take Charla to complete the entire picture, we can first determine how much area she can complete in one hour based on the information provided.
If Charla completes \( \frac{2}{3} \) of the area in \( \frac{1}{2} \) hour, then we can find the rate at which she works:
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In \( \frac{1}{2} \) hour, she completes \( \frac{2}{3} \) of the area. To find her rate per hour, we multiply this by 2: \[ \text{Rate} = \frac{2}{3} \times 2 = \frac{4}{3} \text{ of the area per hour.} \]
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Now, to find out how long it takes her to complete the entire area (1 whole area), we set up the equation: \[ \text{Time} = \frac{\text{Whole area}}{\text{Rate}} = \frac{1}{\frac{4}{3}} = \frac{3}{4} \text{ hours.} \]
Thus, it will take Charla \( \frac{3}{4} \) of an hour to complete the entire picture.