Question

on a map with a scale 1:100,000 the distance between two cities is 12cm. what would be the distance between these two cities on a different map with a scale 1:300,000?

Answer 1

Part 1)

we have

the scale is
`1:100,000`

the distance on a map is
`12\ cm`

we know that

The scale is equal to the distance on a map divided by the real distance

Let

x------> distance on a map

y-------> real distance

S-------> scale

`S=(x)/(y)`

In this part we have

`S=(1)/(100,000)`

`x=12\ cm`

Find the value of y

`y=(x)/(S)`

Substitute the values

`y=(12)/((1/100,000))`

`y=1,200,000\ cm`

Convert to kilometers

`y=12\ Km`

Part 2)

In this part we have

`S=(1)/(300,000)`

`y=12\ km`

Find the value of x

`x=S*y`

Substitute the values

`x=(1/300,000)*12`

`x=0.00004 Km`

Convert to centimeters

`x=4\ cm`

therefore

the answer is

The distance is
`4\ cm`