To find out how long it will take Sharla to complete the entire picture, we first note that she covers \( \frac{2}{3} \) of the area in \( \frac{1}{2} \) hour (30 minutes).
To find the time to complete the whole area, we can set up a proportion based on the area covered:
If \( \frac{2}{3} \) of the area takes \( \frac{1}{2} \) hour, then the whole area (1) would take \( T \) hours. We can set up the following equation:
\[ \frac{\frac{2}{3}}{1} = \frac{\frac{1}{2}}{T} \]
To solve for \( T \), we can cross-multiply:
\[ \frac{2}{3} T = \frac{1}{2} \]
Now, we can isolate \( T \):
\[ T = \frac{1}{2} \div \frac{2}{3} \]
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ T = \frac{1}{2} \cdot \frac{3}{2} = \frac{3}{4} \]
So, it will take Sharla \( \frac{3}{4} \) of an hour to complete the entire picture.
To convert \( \frac{3}{4} \) hours into minutes, we can multiply by 60 minutes per hour:
\[ \frac{3}{4} \times 60 = 45 \text{ minutes} \]
Therefore, it will take Sharla 45 minutes to complete the entire picture.