USING PROPORTIONAL RELATIONSHIPS TO FIND DISTANCE ON A MAP

Example 1 :

The distance between two schools on Lehigh Avenue is shown on the map. If the scale is 1 inch = 2 miles, what is the actual distance between the schools?

Solution :

Step 1 :

Write a proportion using the scale as a unit rate.

Step 2 :

Use the proportion to find the distance.

Because 1 × 3 = 3, multiply 2 by 3.

So, the actual distance between the two schools is 6 miles.

Example 2 :

The distance between Sandville and Lewiston is shown on the map. If the scale is 1 inch = 20 miles, what is the actual distance between the towns?

Solution :

Step 1 :

Write a proportion using the scale as a unit rate.

Step 2 :

Use the proportion to find the distance.

Because 1 × 2.5 = 2.5, multiply 20 by 2.5.

So, the actual distance between the towns is 50 miles.

Example 3 :

The actual distance between two towns is 90 miles. If the scale is 1 inch = 30 miles, what is the distance between the two towns on the map?

Solution :

Step 1 :

Write a proportion using the scale as a unit rate.

Actual distance / map distance = 30/1 = 90/?.

Step 2 :

Use the proportion to find the distance.

30/1 = (30 x 3)/(1 x 3) = 90/3

Because 30 × 3 = 90, multiply 1 by 3.

So, the distance between the towns on the map is 3 inches.

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