Chapter 6.8, Problem 30SR

To determine

To calculate: The actual distance between Columbia and Florence based on map distance.

Answer to Problem 30SR

80 miles.

Explanation of Solution

Given information:

The scale on the map indicates 1inch = 20 miles based on the map of South Carolina.

Calculation:

The actual distance between Columbia and Florence based on map distance is calculated as below,

It is given that every inch of the map actually corresponds to an actual distance of 20 miles. Hence, the ratio is $\frac{1}{20}$ .

The map distance between Columbia and Florence is 4 inches. Let 4 inches be the map distance corresponds to the actual distance assumed to be $x$ miles. Hence, the ratio is $\frac{4}{x}$ .

Algebraically the ratio is getting equated as below,

  $\frac{1}{20}=\frac{4}{x}$

By using the means-extremes property, the values of $x$ is solved as,

  $\frac{1}{20}=\frac{4}{x}$

From the ratio of $\frac{1}{20}=\frac{4}{x}$ , the extreme values are 1 and $x$ & the mean values are 20 and 4.

The product of extremes is equal to the product of means, hence the equation becomes,

  $\begin{array}{l}\frac{1}{20}=\frac{4}{x}\\ x=20\times 4\\ x=80\end{array}$

Hence, 4 inches on the map distance corresponds to the actual distance are 80 miles.

Therefore, the actual distance between Columbia and Florence based on map distance is 80 miles.