Santiago Hampton
01/02/2024 · Primary School
A road crew must repave a road that is \( \frac{7}{8} \) miles long. They can repave \( \frac{1}{56} \) miles each hour. How long will it take the crew to repave the road? Write your answer in simplest form. hours
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Tutor-Verified Answer
Step-by-step Solution
To find out how long it will take the crew to repave the road, we need to divide the total length of the road by the rate at which they can repave.
The total length of the road is \( \frac{7}{8} \) miles, and the crew can repave \( \frac{1}{56} \) miles each hour. We can set up the equation as follows:
\[
\text{Time} = \frac{\text{Total Length}}{\text{Rate}} = \frac{\frac{7}{8}}{\frac{1}{56}}
\]
To divide by a fraction, we multiply by its reciprocal:
\[
\text{Time} = \frac{7}{8} \times \frac{56}{1}
\]
Now, we can simplify this multiplication:
\[
\text{Time} = \frac{7 \times 56}{8 \times 1} = \frac{392}{8}
\]
Next, we simplify \( \frac{392}{8} \):
\[
\frac{392}{8} = 49
\]
Thus, the time it will take the crew to repave the road is
\[
\boxed{49} \text{ hours}.
\]
Quick Answer
It will take the crew 49 hours to repave the road.
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