SOLUTION: The scale of a map is 1:40000. a. Find I killometers, the real distance represented by a distance of 8cm on the map. b.what is the distance of the map represents a real distance

Question 1146569: The scale of a map is 1:40000.
a. Find I killometers, the real distance represented by a distance of 8cm on the map.
b.what is the distance of the map represents a real distance of 5km?
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
The ratio is incompletely given.
1 WHAT to 40000 kilometers?
1 centimeter to 40000 kilometers?

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a. Find I killometers, the real distance represented by a distance of 8cm on the map.
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?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
here's the best reference i could find that makes sense to me.
http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/scale_use.html

the scale that you are referring is called an RF (representative fraction).
the RF tells you the ratio between whatever unit you are dealing with and the comparable unit on the ground.

your problem states:

The scale of a map is 1:40000.
a. Find in kilometers, the real distance represented by a distance of 8cm on the map.
b.what is the distance of the map represents a real distance of 5km?

the scale is 1:40,000.
that says that 1 unit on the map is equal to 40,000 of the same units on the ground.

if you are dealing in cm (centimeters), then 1 centimeter on the map is equivalent to 40,000 centimeters on the ground.

8 centimeters on the map is therefore equal to 8 * 40,000 = 320,000 centimeters on the ground.

1 meter is equal to 100 centimeters.
you would divide centimeters by 100 to get the equivalent measure in meters.
1 kilometer is equal to 1000 meters.
you would divide meters by 1000 to get the equivalent measure in kilometers.
you have 320,000 centimeters.
divide that by 100 and you get 3,200 meters.
divide that by 1000 and you get 3.2 kilometers.
therefore, 8 centimeters on the map is equivalent to 3.2 kilometers on the ground.

you have 5 kilometers on the ground.
multiply that by 1000 to get 5000 meters on the ground.
multiply that by 100 to get 500,000 centimeters on the ground.
the map scale is 1 cm to 40,000 cm.
divide 500,000 cm by 40,000 to get 12.5 cm on the map.

check out the reference.
it's pretty good.
i looked at several before settling on this.
there are also exercises in the reference if you want to test your new found knowledge.

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