Question

A 271⁄2-mile stretch of road needs repaving. A company bid on the repaving project, saying they could repave 21⁄4 miles of road per week. How many weeks will the company take to completely repave the stretch of road? A. 122⁄9 B. 131⁄2 C. 151⁄2 D. 121⁄3

Answer 1

$\text{To repave \frac{21}{4} miles, time needed = 1 week}\\ \\ \text{To repave \frac{271}{2} miles, time}\\ \\ \text{needed }= \frac{271}{2} \div \frac{21}{4} = \frac{271}{2} \times \frac{4}{21} = \frac{542}{21} \: weeks \\ \\ answer = \frac{542}{21} \: weeks$

Answer 2

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$\text{To repave \frac{21}{4} miles, time needed = 1 week}\\ \\ \text{To repave \frac{271}{2} miles, time}\\ \\ \text{needed }= \frac{271}{2} \div \frac{21}{4} = \frac{271}{2} \times \frac{4}{21} = \frac{542}{21} \: weeks \\ \\ answer = \frac{542}{21} \: weeks$

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