Question

ty was making a map of his neighborhood and decided to use the scale of 1 inch : 2 miles. he measured that the distance from his garage to the entrance of the skatepark was 3,520 feet. how far should he make this distance on his map? (note 1 mile = 5,280 feet). write your answer as a fraction.

Explanation:

Step1: Convert feet to miles

First, we know that 1 mile = 5280 feet. So to convert 3520 feet to miles, we divide 3520 by 5280.
$$\frac{3520}{5280}$$
Simplify this fraction by dividing numerator and denominator by 1760: $$\frac{3520\div1760}{5280\div1760}=\frac{2}{3}$$ miles.

Step2: Use the map scale

The scale is 1 inch : 2 miles. Let \( x \) be the distance on the map in inches. We set up the proportion:
$$\frac{1}{2}=\frac{x}{\frac{2}{3}}$$
Cross - multiply: \( 2x=\frac{2}{3}\times1 \)
Then solve for \( x \): \( x = \frac{2}{3}\div2=\frac{2}{3}\times\frac{1}{2}=\frac{1}{3} \)

Answer:

\(\frac{1}{3}\)