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Chapter 1: Problem 13

(a) In track meets both 100 yards and 100 meters are used as distances for dashes. Which is longer? By how many meters is it longer? By how many feet? (b) Track and field records are kept for the mile and the so-called metric mile \((1500 \mathrm{me}-\) ters). Compare these distances.

Short Answer

Expert verified
a) 100 meters is longer than 100 yards by \(8.56\) meters, or approximately \(28.05\) feet. b) A mile is longer than \(1500\) meters (metric mile) by \(109.34\) meters.

Step by step solution

01

Convert Yards to Meters

To compare the first set of distances, the student needs to convert 100 yards into meters. One yard is equal to approximately \(0.9144\) meters, so if we multiply \(100\) by \(0.9144\) we get \(91.44\) meters. So, \(100\) yards is \(91.44\) meters.
02

Compare 100 Yards and 100 Meters

Now, compare \(100\) yards (\(91.44\) meters) with \(100\) meters. Clearly, \(100\) meters is longer. The difference can be calculated by subtracting the converted yard distance from \(100\) meters. The result is \(100 - 91.44 = 8.56\) meters.
03

Convert Meters to Feet

To figure out by how many feet \(100\) meters is longer than \(100\) yards, convert \(8.56\) meters (the difference calculated in the previous step) to feet. One meter is equal to approximately \(3.28084\) feet, so if we multiply \(8.56\) by \(3.28084\), a result of approximately \(28.05\) feet is obtained.
04

Convert Miles to Meters

To compare the distances of a mile and a metric mile (\(1500\) meters), one needs to convert the mile into meters. One mile is approximately equal to \(1609.34\) meters. Therefore, one can assert that a mile is \(1609.34\) meters.
05

Compare Mile and 1500 Meters

Now, compare a mile (\(1609.34\) meters) with \(1500\) meters. Clearly, a mile is longer. The difference can be calculated by subtracting \(1500\) meters from the converted mile distance. The result is \(1609.34 - 1500 = 109.34\) meters.

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