Answer to Question #141249 in General Chemistry for Javier

Question

Two cities A and B are separated by a distance measured in metric units on a map with a scale 1:250,000. The map distance between A and B is 10 cm. What is the ground distance?

Km____________. Miles __________.

Answer 1

Given the distance between two points A and B is 10 cm

Now,

This Ratio of map distance to the corresponding ground distance is independent of units of measurement and is called representative fraction (R.F.)

The scale used has the R.F. value 

          = 1:250,000

           

This means 1 cm in map is equivalent to the 250,000 cm in ground.

I.e.

   1 cm in map = 250,000 cm 

As, 1 cm = 10^–5 Km

1 cm in map = 250,000×10^–5 Km 

Or, 10 cm in map = 250,000×10^–4 Km

Or, 10 cm in map = 25 Km

We know, 1.609 km = 1 Mile

             1 Km =( 1/1.609 ) Mile

             

         So,  25 Km =( 25/1.609 ) Mile

          Or, 25 Km = 15.538 Mile

Hence, The ground distance = 25 Km

   Or, ground distance = 15.538 Mile