To determine how long it will take Charla to complete the entire picture, we can first find the rate at which she covers the area.
Charla completes \( \frac{2}{3} \) of the area in \( \frac{1}{2} \) hour.
Step 1: Find the rate of area covered per hour.
If she completes \( \frac{2}{3} \) of the area in \( \frac{1}{2} \) hour, we can calculate her rate as follows:
\[ \text{Rate} = \frac{\text{Area completed}}{\text{Time}} = \frac{\frac{2}{3}}{\frac{1}{2}} \]
To divide by a fraction, we can multiply by its reciprocal:
\[ \text{Rate} = \frac{2}{3} \times \frac{2}{1} = \frac{4}{3} \]
This means she can complete \( \frac{4}{3} \) of the area in 1 hour.
Step 2: Calculate the total time for the entire area.
Since Charla can complete \( \frac{4}{3} \) of the area in 1 hour, we need to find out how long it takes to complete the whole area (1 full area).
Let \( T \) be the time in hours to complete the entire area:
\[ \text{Rate} \times T = 1 \]
Substituting the rate we found:
\[ \frac{4}{3} \times T = 1 \]
To solve for \( T \):
\[ T = \frac{1}{\frac{4}{3}} = \frac{3}{4} \text{ hours} \]
Step 3: Convert the time into minutes.
To convert \( \frac{3}{4} \) hours into minutes, we multiply by 60 minutes/hour:
\[ \frac{3}{4} \times 60 = 45 \text{ minutes} \]
Conclusion
It will take Charla 45 minutes to complete the entire picture.