Charla wants to cover a certain rectangular area of her driveway with a picture using chalk. If she completes 23 of the area in 12 hour, how long will it take her to complete the entire picture? Enter your answer as a simplified fraction. (1 point)

of an hour

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
4 hours ago

To determine how long it will take Charla to complete the entire picture, we first find out how much area she can cover in one hour.

If Charla completes \(\frac{23}{12}\) of the area in 12 hours, we can calculate the area she completes in one hour by dividing this quantity by 12:

\[ \text{Area per hour} = \frac{23}{12} \div 12 = \frac{23}{12} \times \frac{1}{12} = \frac{23}{144} \]

Now, to find out how long it will take to complete 1 whole area, we take the reciprocal of her hourly rate.

The time \(t\) to complete 1 area is given by:

\[ t = \frac{1 \text{ area}}{\frac{23}{144} \text{ area per hour}} = \frac{144}{23} \text{ hours} \]

Thus, the time it will take Charla to complete the entire picture is:

\[ \boxed{\frac{144}{23}} \text{ hours} \]