1.2.2: Scale Drawings and Maps

Lesson

Let's use scale drawings to solve problems.

Exercise \(\PageIndex{1}\): A Train And a Car

Two cities are 243 miles apart.

• It takes a train 4 hours to travel between the two cities at a constant speed.
• A car travels between the two cities at a constant speed of 65 miles per hour.

Which is traveling faster, the car or the train? Be prepared to explain your reasoning.

Exercise \(\PageIndex{2}\): Driving on I-90

1. A driver is traveling at a constant speed on Interstate 90 outside of Chicago. If she traveled from Point A to Point B in 8 minutes, did she obey the speed limit of 55 miles per hour? Explain your reasoning.
2. A traffic helicopter flew directly from Point A to Point B in 8 minutes. Did the helicopter travel faster or slower than the driver? Explain or show your reasoning.

Figure \(\PageIndex{1}\)

Use the Distance tool to measure the shortest distance between two points.

Exercise \(\PageIndex{3}\): Biking through Kansas

A cyclist rides at a constant speed of 15 miles per hour. At this speed, about how long would it take the cyclist to ride from Garden City to Dodge City, Kansas?

Figure \(\PageIndex{2}\): By skeeze. Public Domain. Pixabay. Source.

Figure \(\PageIndex{3}\): Map with a line, trending downward and right. Endpoints are Garden City and Dodge City. Scale with line segment labeled 4 miles. The distance between the endpoints is about 12 and one half of the scale line segments. By American Fact Finder by the United States Census Bureau. Public Domain. American Fact Finder. Source.

Are you ready for more?

Jada finds a map that says, “Note: This map is not to scale.” What do you think this means? Why is this information important?

Summary

Maps with scales are useful for making calculations involving speed, time, and distance. Here is a map of part of Alabama.

Figure \(\PageIndex{4}\): A map of a part of Alabama. Three points indicate three different cities on the map. The bottom point is labeled Montgomery, the middle point is labeled Centreville, and the top point is labeled Birmingham. A scale on the map shows 1 inch equals 20 miles. The distance between Birmingham and Montgomery is approximately 4 point 5 inches on the map. By United States Census Bureau. Public Domain. American Fact Finder. Source.

Suppose it takes a car 1 hour and 30 minutes to travel at constant speed from Birmingham to Montgomery. How fast is the car traveling?

To make an estimate, we need to know about how far it is from Birmingham to Montgomery. The scale of the map represents 20 miles, so we can estimate the distance between these cities is about 90 miles.

Since 90 miles in 1.5 hours is the same speed as 180 miles in 3 hours, the car is traveling about 60 miles per hour.

Figure \(\PageIndex{5}\): Table with arrows. Time, hours. Data, from top to bottom, 1.5, 3, 1. Distance, miles. Data from top to bottom, 90, 180, 60. On the left and right of the table, two downward arrows labeled times 2 and times one third.

Suppose a car is traveling at a constant speed of 60 miles per hour from Montgomery to Centreville. How long will it take the car to make the trip? Using the scale, we can estimate that it is about 70 miles. Since 60 miles per hour is the same as 1 mile per minute, it will take the car about 70 minutes (or 1 hour and 10 minutes) to make this trip.

Glossary Entries

Definition: Scale

A scale tells how the measurements in a scale drawing represent the actual measurements of the object.

For example, the scale on this floor plan tells us that 1 inch on the drawing represents 8 feet in the actual room. This means that 2 inches would represent 16 feet, and \(\frac{1}{2}\) inch would represent 4 feet.

Figure \(\PageIndex{6}\)

Definition: Scale Drawing

A scale drawing represents an actual place or object. All the measurements in the drawing correspond to the measurements of the actual object by the same scale.

Figure \(\PageIndex{7}\)

Practice

Exercise \(\PageIndex{4}\)

Here is a map that shows parts of Texas and Oklahoma.

Figure \(\PageIndex{8}\): By United States Census Bureau. Public Domain. American Fact Finder. Source.

1. About how far is it from Amarillo to Oklahoma City? Explain your reasoning.
2. Driving at a constant speed of 70 miles per hour, will it be possible to make this trip in 3 hours? Explain how you know.

Exercise \(\PageIndex{5}\)

A local park is in the shape of a square. A map of the local park is made with the scale 1 inch to 200 feet.

1. If the park is shown as a square on the map, each side of which is one foot long, how long is each side of the square park?
2. If a straight path in the park is 900 feet long, how long would the path be when represented on the map?