Question

On the map below 1/4 inch represents one mile. Candler, Canton, and Oteen are three cities on the map. If Candler and Oteen are 3 1/2 inches apart on the map, what is the actual distance between Candler and Oteen in miles?

Answer 1

14 miles

Explanation:

Given:

• 
  `\sf Scale=\frac14\:in : 1\:mile`

• distance between Candler and Oteen is 3 1/2 in

Let
`x` be the distance between Candler and Oteen in miles.

`\implies \frac14:1=3 \frac12:x`

`\implies (\frac14)/(1)=(\frac72)/(x)`

`\implies \frac14x=\frac72`

`\implies x=\frac72 / \frac14`

`\implies x=\frac72 * \frac41`

`\implies x=(28)/(2)`

`\implies x=14`

Answer 2

14 miles

Explanation:

Let "Candler" be known as "C" and "Oteen" as "O"

Given:

• 0.25 inch = 1 mile
• Distance between "C" and "O" (In inches): 3.5 inches

3.5 ------> 3.50

• ⇒ Distance between "C" and "O" (In inches): 3.50 inches

Comparing the rate (inches/mile) and the distance:

• ⇒ 0.25x = 3.50

Multiplying both sides by 100:

• ⇒ 25x = 350

Clearly, 350 is divisible by 25 as "50" is divisible by 25.

Divide both sides by 25 to isolate x:

• ⇒ 25x/25 = 350/25
• ⇒ x = 14

The actual distance between the two cities is 14 miles.