Question

The scale on a map of Virginia shows that $1$ inch represents $30$ miles. The actual distance from Richmond, VA, to Washington, D.C., is $110$ miles. On the map, how many inches are between the two cities?

Answer 1

Hint: In order to solve the given question, we should know that inch and mile are units of distance. Distance can be measured in various units such as inch, kilometer, meter, foot, yard, mile and so on. Various identities are used in order to find out the distance in inches and miles.

Complete step by step solution:
The given question is based on distance. Before starting the question, we should know what is inch and what is mile.
Inch: The inch is a unit of length. One-inch equals $\dfrac{1}{{36}}$ yard.
Mile: Mile is the unit of distance. One-mile equals to $1760$ yards which is equal to $63360$ inches.

One distance unit can be easily converted to another unit. There are certain identities which can be used in order to convert the units.
Given is, $1\;inch = 30\;miles$.
We have to convert $110$ miles into inches. But before that we have to calculate how much$1$mile is equal to.
$30\;miles = 1\;inch \\
\Rightarrow 1\;mile = \dfrac{1}{{30}}\;inch \\ $
Now, for converting $110$ miles into inches, we multiply $110$ with $\dfrac{1}{{30}}$ and we get,
$110\;miles = \dfrac{1}{{30}} \times 110\;inches \\
\Rightarrow 110\;miles = \dfrac{{11}}{3}\;inches \\
\therefore 110\;miles = 3\dfrac{2}{3}\;inches \\ $
Hence, there are $3\dfrac{2}{3}$ inches between two cities.

Note: We have to use identities so that we can easily solve any problem related to conversion of units. The given problem was distance related. Inches should be used for measuring short distances while miles should be used while dealing with geographical distances. Yards can be used to measure larger objects which would be difficult to measure with inches or feet.