Question
Charla wants to cover a rectangular area of her driveway with a picture using chalk. If she completes 2/3 of the area in 1/2 hour, how long will it take her to complete the entire picture? Enter your simplified fraction.
Answers
GPT-4o mini
To find out how long it will take Charla to complete the entire area of the driveway, we can start by considering how much area she completes in a specific time.
Given that Charla completes \( \frac{2}{3} \) of the area in \( \frac{1}{2} \) hour, we can determine how long it takes her to complete the entire area.
1. First, we find the rate at which Charla works. If she completes \( \frac{2}{3} \) of the area in \( \frac{1}{2} \) hour, we can express her work rate as:
\[
\text{Rate} = \frac{\frac{2}{3} \text{ area}}{\frac{1}{2} \text{ hour}} = \frac{2}{3} \div \frac{1}{2}
\]
Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\text{Rate} = \frac{2}{3} \times 2 = \frac{4}{3} \text{ area per hour}
\]
2. Now, we want to find out how long it takes her to complete the entire area, which we can denote as \( 1 \) area. Using the rate we calculated, we set up the equation for the time \( t \):
\[
\text{Time} = \frac{\text{Total Area}}{\text{Rate}} = \frac{1 \text{ area}}{\frac{4}{3} \text{ area per hour}}
\]
This simplifies to:
\[
\text{Time} = 1 \times \frac{3}{4} = \frac{3}{4} \text{ hour}
\]
Thus, it will take Charla \( \frac{3}{4} \) hour to complete the entire picture.
\[
\boxed{\frac{3}{4}}
\]
Given that Charla completes \( \frac{2}{3} \) of the area in \( \frac{1}{2} \) hour, we can determine how long it takes her to complete the entire area.
1. First, we find the rate at which Charla works. If she completes \( \frac{2}{3} \) of the area in \( \frac{1}{2} \) hour, we can express her work rate as:
\[
\text{Rate} = \frac{\frac{2}{3} \text{ area}}{\frac{1}{2} \text{ hour}} = \frac{2}{3} \div \frac{1}{2}
\]
Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\text{Rate} = \frac{2}{3} \times 2 = \frac{4}{3} \text{ area per hour}
\]
2. Now, we want to find out how long it takes her to complete the entire area, which we can denote as \( 1 \) area. Using the rate we calculated, we set up the equation for the time \( t \):
\[
\text{Time} = \frac{\text{Total Area}}{\text{Rate}} = \frac{1 \text{ area}}{\frac{4}{3} \text{ area per hour}}
\]
This simplifies to:
\[
\text{Time} = 1 \times \frac{3}{4} = \frac{3}{4} \text{ hour}
\]
Thus, it will take Charla \( \frac{3}{4} \) hour to complete the entire picture.
\[
\boxed{\frac{3}{4}}
\]