Question

A road map represents an actual distance of \[18\] $km$ by \[1\] $cm$ in it. If a boy drives a road for \[216\] $km$, what would be the corresponding distance covered in the map?

Answer 1

Hint: First we take a variable \[\;x\] as the distance on the map for \[216\] $km$
Here it is given that the actual distance \[18\] $km$ by \[1\] $cm$ represents as a road map and \[216\] $km$ distance covered by a boy.
Based on the direct proportion, applying the relation between a product of extremes and a product of means.
We can find the distance covered in the map for \[216\] $km$

Complete step-by-step answer:
Let \[x\] be the distance on the map for \[216\] $km$.
We use the direct proportional method,
That is the distance on the road is directly proportional to the distance on the map.
\[1:x = 18:216\]
Also we can write that the product of extremes is equal to the product of means.
Here, an extreme is referring to the actual distance of a road map and means refers to the distance covered by a boy.
\[216 \times 1 = 18 \times x\]
In which it turns implies that,
\[x = \dfrac{{216}}{{18}}\]
On further simplification we get the value of \[x\]
\[x = 12\] $cm$

Therefore, the distance covered in the map for \[216\] $km$ is \[12\] $cm$

Note: Here is an important note where the distance on the road is directly proportional to the distance on the map. And another one is that the product of extremes is equal to the product of means. Direct proportion is the relation between two quantities where the ratio of the two is equal to a constant value.