Problem 29 - Prealgebra

Question

Google Earth The Google Earth image shows the western side of The Mall in Washington, D.C. If the scale indicates that one inch is 800 meters and the distance between the Lincoln Memorial and the World War II memorial is \(\frac{17}{16}\) inches, what is the actual distance between the two landmarks? (IMAGE CANNOT COPY)

Step-by-Step Solution

Answer

The actual distance is 850 meters.

Step 1: Understanding the Scale

The scale of the map indicates that every inch represents 800 meters in real life. This scale is crucial for converting the measured map distance into the actual distance.

Step 2: Measure the Distance on the Map

According to the problem, the distance measured on the map between the Lincoln Memorial and the World War II Memorial is \(\frac{17}{16}\) inches.

Step 3: Calculate Real Distance Using the Scale

To find the actual distance, multiply the map distance by the scale factor. The calculation is as follows: \(\frac{17}{16} \text{ inches} \times 800 \text{ meters per inch} = \frac{17 \times 800}{16} \text{ meters}\).

Step 4: Simplify the Calculation

Perform the multiplication and division: \(\frac{17 \times 800}{16} = \frac{13600}{16} \). Simplify this to get \(850\) meters.

Key Concepts

Understanding Map Scale

The concept of map scale is crucial for translating measurements from maps to real-world distances. A map scale indicates the ratio of a distance on the map to the corresponding distance on the ground. For instance, in the exercise, the scale is defined as 1 inch on the map equals 800 meters in reality. This tells us how much smaller the representation on the map is compared to the actual distance.

Map scales can vary depending on the map's purpose. They can be expressed in different ways, such as a ratio (1:10000) or a graphical scale bar. Understanding how to interpret these scales is fundamental when working with maps. A larger scale (like 1:100) shows more detail of a smaller area, whereas a smaller scale (like 1:1000000) covers a larger area with less detail.

Mastering Measurement Conversion

Measurement conversion is a skill that helps interpret distances when working with varied units of measurement. In this particular problem, we're dealing with converting a measurement from inches to meters using a given scale. The conversion involves a few simple mathematical steps.

Here's how to handle this conversion:

• Identify the map scale—1 inch equals 800 meters.
• Measure the distance on the map, which is provided as a fraction of an inch (\(\frac{17}{16}\)).
• Multiply the measured map distance by the scale factor to convert it into real-world units.

By mastering measurement conversion, you will be able to translate any map measurement to its real-world equivalent accurately, making map reading a much easier task.

Mathematics Problem Solving Made Simple

When faced with mathematics problems, like the one given, it's important to have a systematic approach to problem solving. Here’s a simple method to follow:

• Comprehend the problem: Carefully read and understand the details provided in the problem. Identify what is known and what needs to be found.
• Plan your solution: Determine the steps needed to solve the problem. In this case, the understanding of map scale and measurement conversion are crucial.
• Execute the solution: Apply the appropriate mathematical operations, such as multiplication and simplification, to find the answer. For instance, multiplying \(\frac{17}{16}\) inches by 800 meters gives the real distance.
• Review the answer: Once you have a solution, check if the answer makes sense contextually.

Using this structured approach helps break down complex problems into manageable parts, simplifying problem-solving and reducing the chance of errors.