Question

On a map, each inch represents 40 mi. a. If Wichita, Kansas, and Des Moines, Iowa, are approximately 8 in. apart on the map, what is the actual distance between the cities? b. If Seattle, Washington, and Sacramento, California, are approximately $600 \mathrm{mi}$ apart, how many inches would this represent on the map?

Name: Problem 35, Chapter 1: Prealgebra
Uploaded: 2020-07-31T16:28:13-08:00
Duration: 1 min 44 s
Channel: Margaret Farmer
Description: On a map, each inch represents 40 mi. a. If Wichita, Kansas, and Des Moines, Iowa, are approximately 8 in. apart on the map, what is the actual distance between the cities? b. If Seattle, Washington, and Sacramento, California, are approximately 600 mi apart, how many inches would this represent on the map?

   On a map, each inch represents 40 mi.
a. If Wichita, Kansas, and Des Moines, Iowa, are approximately 8 in. apart on the map, what is the actual distance between the cities?
b. If Seattle, Washington, and Sacramento, California, are approximately $600 \mathrm{mi}$ apart, how many inches would this represent on the map?

Prealgebra

Julie Miller, Molly… 1st Edition

Chapter 1, Problem 35

Instant Answer

Solved by Expert Margaret Farmer

07/31/2020

Step 1

We do this by multiplying the number of inches by the number of miles each inch represents. \[8 \text{ inches} \times 40 \text{ miles/inch} = 320 \text{ miles}\] So, the actual distance between Wichita, Kansas, and Des Moines, Iowa is 320 miles. Show more…

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On a map, each inch represents 40 mi. a. If Wichita, Kansas, and Des Moines, Iowa, are approximately 8 in. apart on the map, what is the actual distance between the cities? b. If Seattle, Washington, and Sacramento, California, are approximately $600 \mathrm{mi}$ apart, how many inches would this represent on the map?

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Key Concepts

Map Scale

Map scale is a ratio that relates a distance on a map to the actual distance on the ground. It provides the conversion factor between the measurement on the map and the real world, allowing for accurate distance estimations over geographical areas.

Ratio and Proportion

Ratio and proportion are mathematical concepts used to solve problems where quantities are related in a fixed proportion. In the context of map scales, the proportionality between the map distance and the real-world distance enables the computation of one when the other is known.

Unit Conversion

Unit conversion involves changing a measurement from one unit to another using a conversion factor. In map scale problems, converting measurements such as inches to miles or vice versa is essential for translating map distances into actual distances.

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