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Chapter 1: Problem 5

Horses are to race over a certain English meadow for a distance of 4.0 furlongs. What is the race distance in (a) rods and (b) chains? (1 furlong \(=201.168 \mathrm{~m}, 1\) rod \(=5.0292 \mathrm{~m}\), and 1 chain \(=20.117 \mathrm{~m} .)\)

Short Answer

Expert verified
The distance is approximately 160 rods and 40 chains.

Step by step solution

01

Convert Furlongs to Meters

First, we need to convert the given distance of 4.0 furlongs into meters. We know that 1 furlong equals 201.168 meters. Therefore, the distance in meters can be calculated as follows: \( 4.0 \text{ furlongs} \times 201.168 \frac{\text{meters}}{\text{furlong}} = 804.672 \text{ meters} \).
02

Convert Meters to Rods

Now, we will convert the distance from meters to rods. Since 1 rod equals 5.0292 meters, the number of rods can be calculated by dividing the distance in meters by the meters per rod: \( \frac{804.672}{5.0292} \approx 160 \text{ rods} \).
03

Convert Meters to Chains

Finally, we convert the distance from meters to chains. One chain is 20.117 meters long. Therefore, we calculate the number of chains by dividing the distance in meters by the meters per chain: \( \frac{804.672}{20.117} \approx 40 \text{ chains} \).

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Key Concepts

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

Understanding Furlongs
Furlongs are an interesting unit of measurement with roots in historical English agriculture. They are commonly used in horse racing today. A furlong is defined as 220 yards, which is equivalent to 201.168 meters.
  • Furlongs originated from the Old English 'furh', meaning furrow鈥攖hat is, the length of a furrow in a plowed field.
  • The uses of furlongs were typical for surveying land and defining large areas, especially in agriculture.
  • Remember that there are 8 furlongs in a mile, making it a familiar sight in racing tracks.
In the context of racing, such as in the original exercise, converting furlongs to meters can help better understand distances in modern units. This is essential for ensuring accuracy and consistency when comparing different units of length.
Exploring Rods in Unit Conversion
Rods are a less common unit of measurement today, but they still hold a unique place in certain fields like surveying. One rod equals 5.0292 meters.
  • Historically, rods have been used since at least the 9th century A.D. and frequently appeared in construction documents and maps.
  • They are particularly useful in property boundaries, providing precise measurements over short distances.
  • As a handy tip, there are exactly four rods in one chain, tying these units into a neat system of measurement.
When converting furlongs to rods, as we did in the step-by-step solution, you first transform furlongs into meters, then divide by the length of a rod to derive the number of rods. This two-step process highlights the interconnectedness of different units and ensures proper calculations.
Chains and Their Measurement Role
Chains are a significant unit of measurement primarily used in the United States and Great Britain. A chain is exactly 20.117 meters long.
  • Designed initially by surveyor Edmund Gunter in the 17th century, this unit facilitates easy calculations of land area.
  • A chain's length makes it suitable for use over longer distances compared to rods, often in conjunction with measuring square acres.
  • Remember that there are 10 chains in a furlong, creating a flexible stacking of units that aids in the conversion and understanding of land lengths.
For conversions, like turning furlongs into chains, it's crucial to first convert to meters and then apply the conversion to chains. The accuracy of these conversions is essential, especially in contexts like surveying, where exact boundaries are crucial.

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Most popular questions from this chapter

An astronomical unit (AU) is the average distance between Earth and the Sun, approximately \(1.50 \times 10^{8} \mathrm{~km} .\) The speed of light is about \(3.0 \times 10^{8} \mathrm{~m} / \mathrm{s} .\) Express the speed of light in astronomical units per minute.

The common Eastern mole, a mammal, typically has a mass of \(75 \mathrm{~g},\) which corresponds to about 7.5 moles of atoms. (A mole of atoms is \(6.02 \times 10^{23}\) atoms. In atomic mass units (u), what is the average mass of the atoms in the common Eastern mole?

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A standard interior staircase has steps each with a rise (height) of \(19 \mathrm{~cm}\) and a run (horizontal depth) of \(23 \mathrm{~cm} .\) Research suggests that the stairs would be safer for descent if the run were, instead, \(28 \mathrm{~cm} .\) For a particular staircase of total height \(4.57 \mathrm{~m},\) how much farther into the room would the staircase extend if this change in run were made?
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