Since Charla completes 2/3 of the area in 1/2 hour, this means that she completes 1/3 of the area in 1/2 hour, which can be written as 1/3 * 1/2 = 1/6 of the area in 1/2 hour.
Therefore, it will take Charla 6 * 1/2 = <<6*1/2=3>>3 hours to complete the entire picture. Answer: \boxed{3}.can you explain
Let's suppose that the total area of the picture is represented by "A".
In 1/2 hour, Charla completes 2/3 of the area, which can be written as:
(2/3)*A.
However, the question is asking for the time it takes Charla to complete the entire picture, which is equivalent to the whole area (A) of the picture.
We can write the proportion:
(2/3)*A = (1/2) hour.
To find how much time it will take for Charla to complete the entire picture, we need to isolate the variable A (area of the picture) on one side of the equation.
Dividing both sides of the equation by (2/3), we have:
A = (1/2)/(2/3).
To divide by a fraction, we multiply by its reciprocal, so we can simplify to:
A = (1/2)*(3/2) = 3/4.
This means that Charla completes 3/4 of the picture in 1/2 hour.
Now, we need to find how much time it will take for her to complete the remaining 1/4 of the picture.
We already know that she completes 2/3 of the area (which is equivalent to 3/4 of the picture) in 1/2 hour. So, to find out how much time it will take for her to complete the remaining 1/4 of the picture, we can set up the following proportion:
(2/3) : (1/4) = 1/2 hour : x.
To solve for x, we can cross-multiply:
(2/3)*(1/4) = (1/2)*x,
(2/12) = (1/2)*x,
(1/6) = (1/2)*x,
6/6 = (1/2)*x,
1 = (1/2)*x.
To simplify and isolate x, we can multiply both sides by 2:
2 * 1 = 2 * (1/2)*x,
2 = x.
Therefore, it will take Charla x = 2 hours to complete the remaining 1/4 of the picture.
Adding the time it took her to complete 3/4 of the picture (which was 1/2 hour) to the time it took her to complete the remaining 1/4 of the picture (which was 2 hours), we have a total time of 1/2 + 2 = 2.5 hours = 3 hours (rounded to the nearest whole hour). Answer: \boxed{3}.