To find out how long it will take Charla to complete the entire picture, we can first determine her rate of work.
If Charla completes \( \frac{2}{3} \) of the area in \( 12 \) hours, we can find out how long it takes her to complete the entire area by setting up a proportion.
Let \( t \) be the time (in hours) it takes to complete the whole area. We know:
\[ \frac{2}{3} \text{ (area completed)} = 12 \text{ (hours spent)} \]
We can set up the equation as follows:
\[ \frac{2}{3} \text{ area} = 12 \text{ hours} \]
To find out how long it takes to complete \( 1 \) whole area, we can write this as:
\[ 1 \text{ area} = t \text{ hours} \]
To find \( t \), we can use a cross-multiplication approach from the proportions:
\[ \frac{2}{3} \text{ area} \cdot t \text{ hours} = 1 \text{ area} \cdot 12 \text{ hours} \]
Now, we can solve for \( t \):
\[ \frac{2}{3} t = 12 \]
Multiply both sides by \( \frac{3}{2} \):
\[ t = 12 \cdot \frac{3}{2} = 18 \]
Thus, it will take Charla a total of \( 18 \) hours to complete the entire picture.
Final Answer: 18 hours
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