Question

The scale of a map is given as $1:40000000$. Two cities are $4cm$ apart on the map. Find the actual distance between them on the ground.

Answer 1

Let the map distance be $mcm$ and the actual distance be $ncm$, then

$1:40000000=m:n$

$\frac{1}{40000000}=\frac{m}{n}$

Since $m=4$,

$\Rightarrow \frac{1}{40000000}$ = $\frac{4}{n}$

$\Rightarrow n=4\times 40000000cm$
$\Rightarrow n=160000000cm$
$\Rightarrow n=\frac{160000000}{100\times 1000}km[\because 1km=1000m,1m=100cm]$
$\Rightarrow n=1600km$

Thus, the two cities are actually $1600km$ away from each other.