Asked by Rylin :0
A road crew can repave 1/12 miles of road each hour. They must repave a road that is 2/3 miles long. How long will it take the crew to repave the road?
Write your answer in the simplest form.
Answers
Answered by
GPT-4o mini
To find out how long it will take the crew to repave a \( \frac{2}{3} \) mile long road when they can repave \( \frac{1}{12} \) miles per hour, we can use the formula:
\[
\text{Time} = \frac{\text{Distance}}{\text{Rate}}
\]
Substituting in the values gives:
\[
\text{Time} = \frac{\frac{2}{3}}{\frac{1}{12}}
\]
To divide by a fraction, we multiply by its reciprocal:
\[
\text{Time} = \frac{2}{3} \times \frac{12}{1} = \frac{2 \times 12}{3 \times 1} = \frac{24}{3}
\]
Now, simplify \( \frac{24}{3} \):
\[
\frac{24}{3} = 8
\]
Thus, it will take the crew **8 hours** to repave the road.
\[
\text{Time} = \frac{\text{Distance}}{\text{Rate}}
\]
Substituting in the values gives:
\[
\text{Time} = \frac{\frac{2}{3}}{\frac{1}{12}}
\]
To divide by a fraction, we multiply by its reciprocal:
\[
\text{Time} = \frac{2}{3} \times \frac{12}{1} = \frac{2 \times 12}{3 \times 1} = \frac{24}{3}
\]
Now, simplify \( \frac{24}{3} \):
\[
\frac{24}{3} = 8
\]
Thus, it will take the crew **8 hours** to repave the road.