44. The scale of a map of the Earth reads 1 : 500000. This means that 1 inch on the map is equivalent to 500000 inches on the surface of the Earth. How many miles on the surface of the Earth, to the nearest thousandth, correspond to 2 inches on the map? Note: 1 mile = 1760 yards
Answer: A
15.783 miles
To find the distance on the surface of the Earth that corresponds to 2 inches on the map, we first calculate the actual distance by multiplying 2 inches by the scale factor of 500,000 inches. This results in 1,000,000 inches, which we then convert to miles, yielding approximately 15.783 miles.
A) 15.783 miles
This option is correct as it directly results from the conversion of 1,000,000 inches to miles. To convert inches to miles, we divide by the number of inches in a mile (63,360 inches), yielding 1,000,000 inches ÷ 63,360 inches/mile ≈ 15.783 miles.
B) 189.394 miles
This option is incorrect because it does not reflect the proper conversion from inches to miles based on the scale provided. A miscalculation or misunderstanding of the scale could lead to this figure, but it does not correspond to the 1,000,000 inches calculated from 2 inches on the map.
C) 568.182 miles
This option is also incorrect. Similar to option B, it likely results from an incorrect conversion or misapplication of the scale. The conversion from 1,000,000 inches should give a significantly lower number of miles, as shown in the correct answer.
D) 1000000 miles
This option is incorrect as it vastly overestimates the distance. The calculation clearly shows that 2 inches on the map corresponds to 15.783 miles, not a million miles, indicating a fundamental misunderstanding of the scale.
Conclusion
The correct answer is 15.783 miles, derived from accurate calculations based on the provided map scale. All other options fail to reflect the correct conversion from inches to miles, demonstrating a misunderstanding of the scale and the necessary unit conversions involved.