Question

(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

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

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.

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.

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.

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.

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.

Key concepts

Yards to Meters Conversion

Converting yards to meters is a common task, especially in athletic events that occur in countries using different measurement systems. Knowing the conversion factor is essential. One yard is equivalent to approximately 0.9144 meters.
When you need to convert yards to meters, simply multiply the number of yards by 0.9144. For example, converting 100 yards to meters involves the calculation:

• 100 yards \( \times 0.9144 = 91.44\) meters

This means 100 yards equals 91.44 meters. Comparing this with 100 meters, it is clear that 100 meters is longer by 8.56 meters.
This conversion primarily helps in understanding and converting competitive distances easily. By remembering the conversion factor of 0.9144, comparing track measures becomes straightforward.

Feet to Meters Conversion

To further understand differences in distances, it’s often useful to convert even small measurement differences into more commonly used units, such as feet. A single meter is approximately equal to 3.28084 feet.
To convert meters into feet, multiply the number of meters by 3.28084. For instance, when you have an 8.56-meter difference from our previous step, converting it to feet is as follows:

• 8.56 meters \( \times 3.28084 = 28.05\) feet

This calculation shows that 8.56 meters is about 28.05 feet longer.
Such conversions are often used in practical contexts, such as determining building lengths or athletic track measurements in varying units, making it easier to interpret distances regardless of the systems used.

Miles to Meters Conversion

Miles are often used in contexts like racing and long-distance running events. Converting miles to meters is crucial for comparing events and metrics that differ in system references. One mile equals approximately 1609.34 meters.
To precisely convert miles into meters, multiply the number of miles by 1609.34. For a single mile, the conversion goes:

• 1 mile \( \times 1609.34 = 1609.34\) meters

In the case of comparing 1500 meters to a mile: 1500 meters is noticeably shorter than a mile, with the mile having an edge of 109.34 meters longer.
Understanding this allows athletes and record keepers to clearly gauge distance achievements and set appropriate goals across different measurement standards.