Final answer:
The rates of temperature change with altitude, whether ascending or descending, can be expressed as fractional rates. Ascent corresponds to a decrease in temperature with a rate of -1/50 °F/foot, while descent corresponds to an increase at the same rate of 1/50 °F/foot. These rates are inverse of each other in sign but equal in magnitude.
Step-by-step explanation:
In responding to the student's request for understanding the relationship between altitude and temperature changes, one must first express these changes as rational numbers. For Part A, the change in elevation is +1,000 feet, and the temperature change associated with that elevation change is -20 degrees Fahrenheit. These can be written as the rational numbers 1,000 and -20, respectively.
Part B and Part C require writing a numerical expression for the rate of temperature change in degrees Fahrenheit per foot. This is obtained by dividing the temperature change by the elevation change, which gives us -20°F / 1,000 feet. To express as a fraction, this is −20/1,000, which simplifies to −1/50 degrees Fahrenheit per foot.
For Part D and Part E, considering the reverse situation where the plane descends 1,000 feet and the temperature rises by 20°F, the rate of temperature change would be 20°F / 1,000 feet, or 20/1,000 as a fraction which simplifies to 1/50 degrees Fahrenheit per foot.
Finally, in Part F, the rates from Part C (−1/50) and Part E (1/50) are related by their opposite signs. This means that for every foot of ascent, the temperature decreases at the same rate as it increases for every foot of descent.