Charla wants to cover a certain 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?(1 point)
of an hour
To complete 2/3 of the area in 1/2 hour, it would take Charla (1/2) / (2/3) = (1/2) * (3/2) = 3/4 of an hour.
Therefore, it would take her 3/4 of an hour to complete the entire picture.
To solve this problem, we can use the concept of ratios.
Given that Charla completes 2/3 of the area in 1/2 hour, we can set up a ratio:
2/3 area / 1/2 hour = 1 whole area / x hours
Cross-multiplying, we get:
(2/3) * x hours = (1/2) * 1 whole area
Simplifying, we have:
(2/3) * x = 1/2
To find x, we can multiply both sides by the reciprocal of (2/3), which is (3/2):
(2/3) * x * (3/2) = (1/2) * (3/2)
This simplifies to:
x = 3/4
Therefore, it will take Charla 3/4 of an hour to complete the entire picture.
To find out how long it will take Charla to complete the entire picture, we need to find the proportion between the completed area and the time spent.
Given that she completes 2/3 of the area in 1/2 hour, we can determine her rate of completing the area by dividing the completed area by the time spent.
Rate = Completed area / Time
Rate = (2/3 of the area) / (1/2 hour)
To find the total time required to complete the entire picture, we can set up a proportion using the rate mentioned above:
Rate = (2/3 of the area) / (1/2 hour) = (1 whole area) / (x hours)
Cross multiplying, we get:
(2/3) * (1/2) = 1 / x
Multiplying the numerators and denominators:
2 / 6 = 1 / x
Now, we can solve for x:
2x = 6 * 1
2x = 6
Dividing both sides by 2:
x = 6 / 2
x = 3
Therefore, it will take Charla 3 hours to complete the entire picture.