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

First scale is 1 -> 100,000 each centimeter in map represent 100,000 in the real world.  If you have 12 cm, in reality the distance is (12 cm)(100,000)
12 cm -> 1 200 000 cm,  each m = 100 cm
Distance: 1 200 000 cm / 100 cm/m = 1 200 m
Distance: 1 200 m / 1000 m/km = 1,2 km

Second scale is 1 -> 300,000 each centimeter in map represent 300,000 in the real world.  If you have 12 cm, in reality the distance is (12 cm)(300,000)
12 cm -> 3 600 000 cm,  each m = 100 cm and each km = 1000 m
Distance: 3 600 000 cm / 100 cm/m = 3 600 m
Distance: 3 600 m / 1000 m/km = 3,6 km

300 000 is three times 100 000

The real distance is three times. first case 1,2 second case 3,6

Your anwer is 3,6 in kilometers, 3 600 in meters or 3 600 000 in cm

Answer 2

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

$S=\frac{x}{y}$

In this part we have

$S=\frac{1}{100,000}$

$x=12\ cm$  

Find the value of y

$y=\frac{x}{S}$

Substitute the values

$y=\frac{12}{(1/100,000)}$

$y=1,200,000\ cm$

Convert to kilometers

$y=12\ Km$

Part 2)

In this part we have

$S=\frac{1}{300,000}$

$y=12\ km$  

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 $4\ cm$