To determine how long it will take Charla to complete the entire picture on her driveway, we can first find out how long it takes her to complete \( \frac{2}{3} \) of the area.
Charla completes \( \frac{2}{3} \) of the area in \( \frac{1}{2} \) hour.
To find out how long it will take her to complete the entire area (which is \( 1 \) whole), we can set up a proportion. If \( \frac{2}{3} \) of the area takes \( \frac{1}{2} \) hour, then we can calculate the time \( T \) for the entire area as follows:
\[ T = \frac{1 \text{ (whole area)}}{\frac{2}{3} \text{ (completed area)}} \times \frac{1}{2} \text{ (time taken)} \]
To simplify this, we can calculate the reciprocal of \( \frac{2}{3} \):
\[ \frac{1}{\frac{2}{3}} = \frac{3}{2} \]
Now substituting this back into the equation for \( T \):
\[ T = \frac{3}{2} \times \frac{1}{2} \]
Multiplying these together:
\[ T = \frac{3 \times 1}{2 \times 2} = \frac{3}{4} \text{ hours} \]
Now, converting \( \frac{3}{4} \) hours into minutes (since \( 1 \) hour is \( 60 \) minutes):
\[ \frac{3}{4} \text{ hours} = \frac{3 \times 60}{4} = 45 \text{ minutes} \]
Thus, it will take Charla \( \boxed{45} \) minutes to complete the entire picture on her driveway.
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