Question

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.

Answer 1

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.