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Chapter 2: Problem 9

Which is longer: a 1 -mile race or a 1500 -meter race? Show your reasoning.

Short Answer

Expert verified
The 1-mile race is longer than the 1500-meter race.

Step by step solution

01

Understanding the problem

First, we need to determine the length of both races in the same unit of measurement to compare them directly. We'll compare the length of a 1-mile race with a 1500-meter race.
02

Convert mile to meters

We need to convert the distance of the 1-mile race into meters. 1 mile is equal to approximately 1609.34 meters. Therefore, a 1-mile race is 1609.34 meters long.
03

Compare the distances

Now, we compare the two distances in meters. A 1-mile race is 1609.34 meters. A 1500-meter race is, by definition, 1500 meters. Since 1609.34 meters (the length of a 1-mile race) is greater than 1500 meters (the length of a 1500-meter race), the 1-mile race is longer.

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Key Concepts

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

Measurement Comparison
When comparing measurements, the key is to ensure both quantities are expressed in the same units. This makes it easier to identify which quantity is larger or smaller. In the context of our exercise, the measurements are the lengths of two races, one in miles and the other in meters. By converting the mile measurement to meters, we align both races to the same unit, facilitating a straightforward comparison.

Here鈥檚 a simple method to follow when comparing measurements:
  • Select the unit of measure you want to use for both quantities.
  • Convert any different units to this chosen unit.
  • Compare the resulting values directly.
This process is essential when determining relationships between different quantities, ensuring accuracy in your analysis.
Distance Conversion
Distance conversion is a crucial skill, especially when dealing with international measurements or measurements that need comparison. Conversion entails changing one measurement from its existing unit to another. In our exercise, we converted a distance from miles to meters.

To convert miles to meters, you use the conversion factor where 1 mile is equal to 1609.34 meters. So, if you have the distance in miles, you multiply it by this factor to get the distance in meters. Here's the formula: \[ \text{Distance in meters} = \text{Distance in miles} \times 1609.34 \] This approach ensures that the distances are accurately represented in the units relevant to your comparison.
Mathematics Problem Solving
Mathematics problem-solving often involves different steps, starting from understanding the problem to finding a solution. Let鈥檚 take a look at how we approached our exercise:

  • Understand and define the problem: Recognize that the problem involves comparing two distances given in different units.
  • Identify necessary conversions: Decide which units to convert and calculate the conversions accurately.
  • Evaluate and compare: Once the distances are in the same unit, compare them to determine which is greater.
This structured approach to solving problems is invaluable. By systematically addressing one issue at a time, you increase your understanding and efficiency. Each step builds on the previous one, leading you to a logical conclusion.

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Most popular questions from this chapter

Peter and Seija evaluated the expression \(37+8 \cdot \frac{6}{2}\), Peter said the answer was 135 . Seija said it was 61 . Who is correct? What error did the other person make?

A group of students measured several objects around their school in both yards and meters. $$ \begin{aligned} &\text { Measurement in Yards and Meters }\\\ &\begin{array}{|l|l|l|l|l|l|c|} \hline \text { Yards } & 7 & 3.5 & 7.5 & 4.25 & 6.25 & 11 \\ \hline \text { Meters } & 6.3 & 3.2 & 6.8 & 3.8 & 5.6 & 9.9 \\ \hline \end{array} \end{aligned} $$ a. Use their data, shown in the table, to find a conversion factor between yards and meters. Use the conversion factor to answer these questions: b. The length of a football field is 100 yards. How long is it in meters? (a) c. If it is 200 meters to the next freeway exit, how far away is it in yards? d. How many yards long is a 100 -meter dash? e. How many meters of fabric should you buy if you need 15 yards?

List these fractions in increasing order by estimating their values. Then use your calculator to find the decimal value of each fraction. a. \(\frac{7}{8}\) b. \(\frac{13}{20}\) c. \(\frac{13}{5}\) d. \(\frac{52}{25}\)

Tab and Crystal both own cats. a. Tab buys a 3 -pound bag of cat food every 30 days. At what rate does his cat eat the food? (a) b. Crystal buys a 5 -pound bag of cat food every 45 days. At what rate does her cat eat the food? c. Whose cat, Tab's or Crystal's, eats more food per day? ( \()_{0}\)

This problem is sometimes called Einstein's problem: "Use the digits \(1,2,3,4,5,6,7,8,9\) and any combination of the operation signs \((+,-,, /)\) to write an expression that equals 100 . Keep the numbers in consecutive order and do not use parentheses." Here is one solution: $$ 123-4-5-6-7+8-9=100 $$ Your task is to find another one.
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