Question

This doesn't make any sense to me

You are using a topographic map to do field work in mountainous terrain. You need to hike over that ridge to get to the field area that you are interested in. The trail to the place you want to be is about 5 inch on the map, which has a scale of 1:24000. (Round to two decimal places.)

How many miles does 5 inches on the map represent? _______mi
How many kilometers does 5 inches on the map represent? _____________ km
How many meters does 5 inches on the map represent? _____________m

Answer 1

The scale is just a ratio of units on the map to units on the earth. So, no matter what units I'm given, I can multiply by (in this case) 24000 to get the distance on earth.
\[5 inches \times 24000 = 120000 inches\]
I know that the distance on earth is 120,000 inches, but because the problem asks for miles, I need to convert. I do this by multiplying conversion factors to the amount in inches. Since 1 ft= 12 inches and 1 mi = 5280 feet, I write
\[120,000 inches \times \frac{ 1 ft }{ 12 inches} \times \frac{ 1 mi }{ 5280 ft } \approx 1.89 mi\]The same process can be done in the next 2 problems by use of the apporpriate conversion factors.

Answer 2

so does my answer need to round 2 decimal places?

Answer 3

got it. Thanks a bunch!