Question

Oak Grove and Salem are 87 mi from each other. How far apart would the cities be on a map that has a scale of 5 in : 29 mi?

Answer 1

Hint: In this question, we are given the distance between two cities in miles and a map which has a scale as a ratio of inches and miles. As we are given the relation between the two units so we can convert any value of one unit to the other by using the given scale. Thus, we can find the distance between the two cities in inches when its distance in miles is known.

Complete step-by-step solution:
The map has a scale of 5 in : 29 mi
That is we can measure the distance between both miles and inches from the map. As we are given the distance in miles, we have to find the distance in inches from the above scale. We see that $87 = 3 \times 29$
So, on multiplying the given ratio by 3, we get –
$
 \Rightarrow 5 \times 3\,in:29 \times 3\,mi \\
   \Rightarrow 15\,in:87\,mi \\
 $

Hence the cities are 15 in apart.

Note: The ratio of any two terms remains constant if we multiply both the terms of the ratio by the same value. A ratio is actually a fraction, the first term is the numerator of the fraction and the second term is the denominator of the fraction. We know that we cancel out the common factors to simplify a fraction, so if we multiply the numerator of a fraction by a number, then we have to multiply the denominator with that number too.