Question

Charla wants to cover a certain rectangular area of her driveway with a picture

using chalk. If she completes of the area in hour, how long will it take her to
complete the entire picture?

Answer 1

It will take Charla
`\((3)/(4)\)` hour or
`\(45\)` minutes to complete the entire picture.

Let
`\(t\)` represent the total time (in hours) it takes Charla to complete the entire picture.

She completes
`\((2)/(3)\)` of the area in
`\((1)/(2)\)` hour.

The rate at which she completes the picture is given by the ratio of the completed area to the time:

`\[ \text{Rate} = \frac{\text{Completed Area}}{\text{Time}} \]`

For the partial completion, the rate is:

`\[ \text{Rate}_{\text{partial}} = ((2)/(3))/((1)/(2)) \]`

Now, for the entire completion, the rate should remain the same:

`\[ \text{Rate}_{\text{total}} = (1)/(t) \]`

Setting the rates equal to each other:

`\[ ((2)/(3))/((1)/(2)) = (1)/(t) \]`

Simplify the left side:

`\[ (2)/(3) * (2)/(1) = (4)/(3) \]`

So, the equation becomes:

`\[ (4)/(3) = (1)/(t) \]`

Now, solve for
`\(t\)`:

`\[ t = (3)/(4) \]`

Therefore, it will take Charla
`\((3)/(4)\)` hour or
`\(45\)` minutes to complete the entire picture.

The probable question may be: "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?"