Question

Olympic athletes compete in a 1500-meter event, but not in a mile event. Which race is shorter: 1500 meters or 1 mile? (Given: \(1 \mathrm{mi}=1.61 \mathrm{~km}\).

Short answer

The 1500-meter race is shorter.

Step-by-step solution

Understand the Problem

The problem asks us to compare the lengths of two races: one is 1500 meters, and the other is 1 mile. Our task is to determine which one of these distances is shorter.

Convert Miles to Kilometers

We know that 1 mile is equal to 1.61 kilometers, as given in the problem. Therefore, we need to convert miles to meters since the other distance is given in meters.

Convert Kilometers to Meters

Since 1 kilometer is equal to 1000 meters, we convert 1.61 kilometers to meters:\[1.61 \text{ kilometers} = 1.61 \times 1000 \text{ meters} = 1610 \text{ meters}\]

Compare the Distances

Now that both distances are in meters, we can compare them easily: - 1500 meters - 1610 meters Since 1500 meters is less than 1610 meters, the 1500-meter race is shorter than the 1-mile race.

Key concepts

Distance Comparison

When comparing distances, it is crucial to have both measurements in the same unit to make an accurate comparison. In this exercise, we are comparing a race of 1500 meters to a race of 1 mile. However, since the two utilize different units of measurement, our initial task is to convert them to a common unit. This ensures clarity and prevents errors in analysis. Once both distances are in meters, you can see directly which is shorter or longer. In this case, 1500 meters is less than 1610 meters, indicating that the 1500-meter race is shorter than the mile race. Being able to convert and compare distances in the same unit is a valuable skill in many real-world applications, such as engineering, construction, and academia.

Metric System

The metric system is an international decimalized system of measurement that is widely used around the world for scientific and everyday measurements. It is built on units based on powers of ten, making conversion straightforward. For example, 1 kilometer is equal to 1000 meters, and 1 meter is equal to 100 centimeters. This simplicity is one of the reasons it's preferred globally in science and mathematics fields. In our exercise, understanding that 1 kilometer equals 1000 meters is essential for completing the conversion from kilometers to meters. By converting a mile to meters via kilometers, we use the metric system's ease of conversion to accurately assess the length of both races.

Problem Solving

Problem-solving in the context of unit conversion and measurement comparison involves several steps:

• Understanding the Problem: First, clearly state what you need to find out. Identify both quantities that need comparison.
• Gathering Data: Convert any given information into a more usable form within the context of the problem, using known conversion factors.
• Executing the Conversion: Apply the conversions on all necessary steps, ensuring consistency and accuracy.
• Comparison: Finally, interpret the converted data to arrive at a conclusion about the problem at hand.

Using these steps helps not just in academic problems, but also in practical situations like financial budgeting, cooking, and logistics planning. Critical thinking and methodical processing are key components to successfully solving problems via unit conversion.