Question

The scale of a map is \[1:4000000\]. What is the actual distance between the two towns if they are 5 cm apart on the map?

Answer 1

Hint: Here, we will find the scale of the given representative fraction and then find the real distance of the two cities. We will get the result in centimeters and then we will convert it into km to find the required answer.

Complete step by step answer:

We are given that the representative fraction is \[1/4000000\].

We know that the representative fraction is the ratio of map distance to the corresponding ground distance is independent of units of measurement.

This implies that 1 cm on the map is actually a 4000000 cm distance.

First, we will find the real distance if they are 5 cm apart in the map, we get

\[ \Rightarrow 5 \times 4000000 = 20,000,000{\text{ cm}}\]

Now we will convert this into m as \[1{\text{ m}} = 100{\text{ cm}}\].

\[20,000,000 \times \dfrac{1}{{100}}{\text{ m}} = 200,000{\text{ m}}\]

Converting this above value into km as \[1{\text{ km}} = 1000{\text{ m}}\].

\[200,000 \times \dfrac{1}{{1000}}{\text{ km}} = 200{\text{ km}}\]

Thus, the actual distance between two towns is 200 km.

Note: In this question, students are supposed to scale the representative fraction properly. Also, some students forget to take care of the scales, kilometers, meters, and centimeters. Students should not forget to convert the distance into km or else the answer will be wrong.