Final answer:
The RF scale for '1 inch equals a mile' is 1:63,360. Proportions are used to calculate distances using a map scale, such as converting inches on a map to actual miles, or vice versa, based on the specified scale.
Step-by-step explanation:
The RF (Representative Fraction) scale for the verbal scale '1 inch equals a mile' is expressed as 1:63,360 because there are 63,360 inches in a mile (since 1 mile = 1.61 km and 1 inch = 2.54 cm, it follows that 1 mile = 160934.4 cm, which equals 63,360 inches when divided by 2.54 cm/inch). When calculating distances using a scale, proportions are typically set up to find out the actual distances or map measurements.
For instance, if the scale of a map is 1 inch equals 5.5 miles, to find out how many inches on the map represent 16.5 miles, you would set up the proportion as follows:
- 1 inch / 5.5 miles = x inches / 16.5 miles
After cross-multiplication and division, you would find that x equals 3 inches (since 1 inch / 5.5 miles = 3 inches / 16.5 miles).
In a similar manner, you would calculate the scale measurements for other given actual distances or the actual distances for given scale measurements, as per the specific scale provided in each example or exercise.