Question

The scale of a map is given as $1:30000000$. Two cities are 4 cm apart on the map. Find the actual distance between them.

Answer 1

Hint: We first need to define how the distance in the map works. We find the relation between map unit distance and actual real-life distance from the ratio of $1:30000000$. We use a unitary method to find the distance between two cities which are 4 cm apart on the map. We use multiplication to find the solution of the map.

Complete step by step answer:
In a map the actual distances between any two points is always minimized to a distance that is displayable in the map.
This scaling down of distance is done to accommodate all the places in a single map.
Here it’s given that the scale of a map is given as $1:30000000$ which means that $30000000$ unit distance in real life has been scaled down to 1 unit in the map.
So, 1-unit distance in the map equals to $30000000$ unit distance in the real-world distance.
We need to find the actual distance between two cities which are 4 cm apart on the map.
Using the unitary method, we get to know the distance by multiplying 4 with $30000000$.
So, the distance becomes $4\times 30000000=120000000$ cm.
Now we need to convert the unit from cm to km.
So, $120000000=\dfrac{120000000}{100000}=1200$ km.

The actual distance between two cities is 1200 km.

Note: The unit in the real-life case has to be similar to the map unit. We can convert after getting the value in that specific unit. Ratio of two things is possible only when the units in both cases are the same.