Fill in the blank
Charlie 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
______ of an hour
1 hour
To find the answer, we can set up a proportion:
(2/3 area) : (1/2 hour) = (1 area) : (x hours)
To find the missing value, we can cross-multiply:
(2/3)(x hours) = (1/2)(1 area)
Simplifying, we have:
2x/3 = 1/2
Cross-multiplying again:
4x = 3
Dividing both sides by 4:
x = 3/4
Therefore, it will take Charlie 3/4 of an hour to complete the entire picture.
To find how long it will take Charlie to complete the entire picture, we need to determine the proportion of the area she completes in a given time and use that to calculate the total time.
Given that she completes 2/3 of the area in 1/2 hour, we can set up a proportion:
(2/3) area = (1/2) hour
To find the remaining 1/3 of the area, we can set up another proportion using the same ratio:
(1/3) area = x hours (the time needed to complete the remaining 1/3 of the area)
Now we can solve for x by cross-multiplying:
(2/3) * 1/2 = (1/3) * x
Multiplying both sides:
(2/6) = (x/3)
Reducing fractions:
1/3 = (x/3)
Canceling out the common factor of 3:
1 = x
So, the remaining 1/3 of the area will take Charlie 1 hour to complete. Answering the question directly, it will take her "1" hour to complete the entire picture.
Thus, the blank can be filled as follows:
"1 hour"