Chapter 12, Problem 8PSQ

To determine

To find: The actual distance.

Answer to Problem 8PSQ

The actual distance is $6\text{ miles}$ .

Explanation of Solution

Given information: A map has a scale of $1\text{ inch : 24 miles}$ .The map distance is $\frac{1}{4}\text{ inch}$ .

Calculation: The scale of the map is $1\text{ inch : 24 miles}$ and the map distance is .

Here, The scale of the map is the ratio of the map distance and the actual distance.

Let, the actual distance is $x$ .

Therefore, $\frac{1}{4}\text{ inch : }x\text{ =}$

  $1\text{ inch : 24 miles}$ $\mathrm{......}(1)$

Let’s find the value of $x$ from equation $(1)$ ,

  $\begin{array}{c}\frac{1}{4}\text{ inch : }x\text{ = }1\text{ inch : 24 miles}\\ \frac{\frac{1}{4}\text{ inch}}{x}\text{= }\frac{1\text{ inch}}{24\text{ miles}}\\ \frac{1}{4\times x}\text{ = }\frac{1}{24\text{ miles}}\\ 4x\text{ = 24 miles}\\ x\text{ = }\frac{24}{4}\text{ miles}\\ x\text{ = 6 miles}\end{array}$

Hence, The actual distance is $6\text{ miles}$ .