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While driving in an exotic foreign land you see a speed limit sign on a highway that reads \(180,000\) furlongs per fortnight. How many miles per hour is this? (One furlong is \(\frac{1}{8}\) mile, and a fortnight is 14 days. A furlong originally referred to the length of a plowed furrow.)

Short Answer

Expert verified
The speed limit is approximately 66.96 miles per hour.

Step by step solution

01

Convert Furlongs to Miles

We know that one furlong is \(\frac{1}{8}\) of a mile. Therefore, to convert 180,000 furlongs to miles, we perform the following calculation: \[ \text{Miles} = 180,000 \times \frac{1}{8} = 22,500 \text{ miles}. \]
02

Convert Fortnights to Hours

A fortnight is equal to 14 days. Since each day has 24 hours, a fortnight has \(14 \times 24 = 336\) hours.
03

Determine Miles per Hour

Now, we need to convert miles per fortnight to miles per hour. We use the number of miles calculated in Step 1 and the number of hours calculated in Step 2: \[ \text{Miles per hour} = \frac{22,500 \text{ miles}}{336 \text{ hours}} \approx 66.96 \text{ miles per hour}. \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Furlongs
Furlongs are a somewhat old-fashioned distance measurement. They originate from agricultural terms used to measure the length of plowed furrows in fields. A single furlong is equal to 220 yards or, more commonly in today's usage, \( rac{1}{8} \, ext{of a mile} \). This makes it a rather convenient unit for dividing larger distances, especially when considering racecourses or traditional land measurements.
Although not commonly used in everyday conversation anymore, furlongs might still pop up in specific contexts like horse racing, where racetracks are often measured in furlongs. Understanding this unit helps appreciate historical measurements and adjust them into more modern contexts.
  • 1 furlong = 220 yards
  • 1 furlong = \( rac{1}{8} \, ext{mile} \)
Miles per hour
Miles per hour, commonly abbreviated as mph, is a unit that measures speed by evaluating how many miles are covered in one hour. This unit is prevalent in countries that use the imperial system, such as the United States and the United Kingdom.
Speed limits on roads are usually denoted in miles per hour, and knowing how to convert other speed units to mph can be incredibly beneficial for travelers and drivers. Understanding mph is not only useful for practical purposes like driving but also gives insights into speed comparisons across different domains like sports or animal speeds.
  • Speed conversion helps in understanding travel time and distance.
  • Miles per hour is often used in road signages in certain countries.
Conversion Factors
Conversion factors are essential mathematical tools that allow us to transform one unit of measure to another. To use conversion factors, we often multiply the quantity in one unit by a fraction equivalent to 1 (the conversion factor), allowing us to seamlessly switch between metric and imperial systems, or other units altogether.
In our example, converting furlongs to miles was achieved by multiplying the number of furlongs by the conversion factor \( rac{1}{8} \, ext{mile per furlong} \). Similarly, converting fortnights to hours involved using the conversion factor \( 336 \, ext{hours per fortnight} \). Mastery over these factors simplifies complex conversions, ensuring accurate and precise unit transformations.
  • Helps in converting between different units.
  • Utilizes fractions to ensure accurate conversion without losing value.
  • Essential for mathematical precision in science and everyday calculations.

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