Answer to Question #102870 in Physical geography for Taylor White

Question

1. One meter equals 177 miles
Convert to a representative fraction

2.The following USGS topographic map of The Dalles, Oregon has a scale of 1/24000. What would be the distance in centimeters on the actual ground if you traveled five inches on the map?

3.One centimeter equals one mile
Convert to a representative fraction

4. The distance between Cincinnati and Columbus is 107 miles. You have a map with a scale of 1/75000. What is the distance in centimeters on the map between the two cities?

5. One centimeter equals 100,000 kilometers
Convert to a representative fraction

Answer 1

1. We can write 1:1.77 and state that 1 centimeter on map corresponds to 1.77 miles on real land, but this representation is not correct as it contains different units. Therefore, convert 177 miles to meters by multiplying 177 by 1609:

$$177\text{ mil}\cdot1609\text{ m/mil}=284793\text{ m}.$$

Therefore, R.F. will be

$$1:284793,$$

i.e. 1 meter on map represents 284793 meters on land.

2. Assume that 1/24000 means that 1 centimeter on map relates to 24 000 meters on land. Five inches on map will be

$$5\text{ inch}\cdot2.54\text{ cm/inch}=12.7\text{ cm}.$$

Therefore, on land we would travel a distance of

$$D=12.7\cdot24000=304800\text{ m}.$$

3. One centimeter is one-hundredth of meter. One mile is 1609 meters. Therefore, the representative fraction will be

$$1:1609.$$

4. 107 miles is (multiplied by 1609 m/mil) 172163 meters. Therefore, on the map this distance will be (if the scale is 1 cm per 75000 meters)

$$172163/75000=2.3\text{ cm}.$$

5. One kilometer is 1000 meters. 1 meter is 100 centimeters. Therefore, 1 km is

$$100\cdot1000=100000\text{ cm}.$$

In centimeters the representative fraction will be

$$1:10^{10}=1:10\space000\space000\space000.$$