Question

A scale on a map shows that 2 inches equal to 25 miles. How many inches on the map represent 60 miles?

Answer 1

Hint: We convert the given ratio of the distances in the map and the actual distance in the form of proportionality. We take an arbitrary constant. We use the given values of the variables to find the value of the constant. Finally, we put the constant’s value to find the equation along with the unit in quarts.

Complete step by step answer:
We have been given the relation between two variables where we assume the distance in actual length as r and the respective distance in the map as p.
The relation between r and p is a direct relation.
It’s given r varies directly as p which gives $r\propto p$.
To get rid of the proportionality we use the proportionality constant which gives $r=kp$.
Here, the number k is the proportionality constant.
It’s given $r=25$ when $p=2$.
We put the values in the equation $r=kp$ to find the value of k.
So, $25=k\times 2$. Simplifying we get \[k=\dfrac{25}{2}\].
Therefore, the equation becomes with the value of k as $r=\dfrac{25}{2}p$.
Now we simplify the equation to get the value of p for actual distance in real life being 60
\[\begin{align}
  & 60=\dfrac{25}{2}p \\
 & \Rightarrow p=\dfrac{2\times 60}{25}=4.8 \\
\end{align}\]

Therefore, 60 miles is represented by \[4.8\] inches in the map.

Note: In a direct proportion, the ratio between matching quantities stays the same if they are divided. They form equivalent fractions. In an indirect (or inverse) proportion, as one quantity increases, the other decreases. In an inverse proportion, the product of the matching quantities stays the same.