The distance between 2 cities is 120km. If the map

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The distance between 2 cities is 120km. If the map scale is 1 : 800 000, find the distance between those 2 cities on the map ( in cm )Bantu

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The distance between those 2 cities on the map is 15 cm.
 

Explanation

Scale (map)

Given:

The distance between 2 cities is 120 km.
The scale of the map is 1 : 800000.

Let $d$ be the “real“ distance, $s$ be the scale factor of the map, and $d'$ be the scaled distance on the map.

Thus:

$\begin{aligned}\bullet\ &d=120\rm\ km=120\times10^5\rm\ cm\\ \bullet\ &s=1:800000=1:\left(8\times10^5\right)\\&\Rightarrow s=\frac{1}{8\times10^5}\end{aligned}$

Solving it for $d'$ :

$\begin{aligned}d'&=d\times s\\&=\left(120\times10^5\times\frac{1}{8\times10^5}\right)\rm\ cm\\&=\frac{120\times\cancel{10^5}}{8\times\cancel{10^5}}\rm\ cm\\&=\frac{120}{8}\rm\ cm\\\therefore\ d'&=\boxed{\ \bf15\ cm\ }\\\end{aligned}$