Question

On a particular road map, $\dfrac{1}{2}$ inch represents 18 miles. About how many miles apart are 2 towns that are $2\dfrac{1}{2}$ inches apart on this map?
(a) 25 miles
(b) 90 miles
(c) 110 miles
(d) None of these

Answer 1

Hint: In this problem we are given a particular road map, where we are trying to find the distance between two cities using the given conditions. We are told $\dfrac{1}{2}$ inch represents 18 miles in the map and we are to find the distance from two towns which are $2\dfrac{1}{2}$ inches apart. We can put the values in a ratio form to find the distance and calculate that we can get our needed solution.

Complete step by step solution:
According to the problem, we are given a proportional map where inches and miles are given as a ratio.
To start with, we have, $\dfrac{1}{2}$ inch represents 18 miles.
Thus, following this, we get 1 inch representing 36 miles.
Now, we have to find out how many miles apart are two towns if they are $2\dfrac{1}{2}$ inches apart on this map.
So, we can also set up a proportion below:
$\dfrac{\dfrac{1}{2}}{18}=\dfrac{2\dfrac{1}{2}}{x}$
Now, simplifying,
$\dfrac{0.5}{18}=\dfrac{2.5}{x}$
Then, trying to get the value of x and cross multiplying,
$\Rightarrow 0.5\times x=2.5\times 18$
Dividing both sides by 0.5, we are getting, $x=\dfrac{2.5\times 18}{0.5}$
So, we have the value of x as, x = 90.

So, the correct answer is “Option B”.

Note: This is a typical type of problem which is called a map ratio problem. For solving these problems, we are to take care of the ratio – map scale, then the values in proper places would give us the solution. And the thing we need to keep in mind is that, the ratio is always to be written in the simplest form.