Problem 50 - Chemistry The Science in Context

Question

Olympic Mile An Olympic "mile" is actually \(1500 \mathrm{m}\). What percentage is an Olympic mile of a U.S. mile (5280 feet)?

Step-by-Step Solution

Answer

Answer: An Olympic mile is approximately 93.201% of a U.S. mile.

Step 1 - Convert the distances to the same units

First, we need to convert the U.S. mile to meters, since the Olympic mile is given in meters. We know that 1 meter is equal to 3.28084 feet. So, to convert 5280 feet to meters, we can use the following formula: Meters = Feet / 3.28084 Plug in the values: Meters = 5280 / 3.28084

Step 2 - Perform the conversion calculation

Now we can calculate the value of a U.S. mile in meters: Meters = 5280 / 3.28084 ≈ 1609.344 Therefore, a U.S. mile is approximately 1609.344 meters.

Step 3 - Find the percentage of the Olympic mile to the U.S. mile

Now we have both distances in meters and can calculate the percentage. To find the percentage, we use the following formula: Percentage = (Olympic mile / U.S. mile) × 100 Plug in the values: Percentage = (1500 / 1609.344) × 100

Step 4 - Calculate the percentage

Now we can calculate the percentage: Percentage = (1500 / 1609.344) × 100 ≈ 93.201 Thus, an Olympic mile is approximately 93.201% of a U.S. mile.

Key Concepts

Distance Conversion

Understanding how to convert one unit of distance to another is crucial when comparing measurements across different systems. Imagine you have the distance for an Olympic mile given in meters, but you want to compare it to a U.S. mile, which is in feet. To accurately compare these, we must convert one of them so that both distances are in the same unit.

• The first step is to identify the conversion rate. Knowing that 1 meter equals approximately 3.28084 feet, we can use this conversion rate to translate U.S. miles into meters.
• To convert feet to meters, use the formula: Meters = Feet / 3.28084.

To give you a practical example, when you apply this formula to 5280 feet (one U.S. mile), you find it equals approximately 1609.344 meters. Converting measurements helps you see how different units can relate to each other, allowing for better comparisons and understanding.

Olympic Mile

The term "Olympic mile" can be a little misleading because it's not exactly a standard mile measurement. It actually refers to a distance of 1500 meters.
This metric measurement is often used in track racing events, especially those associated with the Olympics.
The Olympic mile is shorter than both a U.S. mile and an exact true mile which is traditionally 1609.344 meters.

• An Olympic mile is set at 1500 meters, which is convenient for the simplicity of metric measurements.
• When engaging in sports or international athletic events, the metric system is commonly used because of its universality and ease of calculation.

Understanding the Olympic mile is crucial for athletes and enthusiasts who need to translate their performance or training results into the terms familiar to their international competitions.

Measurement Comparison

Comparing measurements requires more than just lining up the numbers—it's about understanding and transforming those numbers into comparable units so they can tell a useful story. In the exercise, we want to compare an Olympic mile to a U.S. mile to find out what percentage the former is of the latter.
Here's how to do it:

• Once you have converted both units to the same system, in this instance by converting the U.S. mile to meters, you can perform a comparison.
• Use the formula: Percentage = (Olympic mile / U.S. mile) × 100 to find how much of one measurement is contained within the other.

In the exercise example, the Olympic mile is approximately 93.201% of a U.S. mile. This means the Olympic mile is shorter but relatively close to the length of a U.S. mile, demonstrating professional athletes' considerable endurance in meters compared to feet. Understanding this percentage helps in many fields ranging from sports science to international travel prediction logs, seamlessly blending different measurements into practical information.