Question

A race pilot's average rate of speed over a 720-mile course is inversely proportional to the time in minutes t the pilot takes to fly a complete race course. The pilot's final score s is the average speed minus any penalty points p earned. 1. Write a function to model the pilot's score for a given t and p (Hint: d = rt) 2. Graph the function for a pilot who has two penalty points. 3. What is the maximum time a pilot with 2 penalty points can take to finish the course and still earn a score of at least 3?

Answer 1

If d = rt,  Then r = d/t
avg speed = 720/t

Therefore after subtracting penalty points, the function for score is:
$s = \frac{720}{t} - p$

For part 2 i will attach a picture.


Part 3)
Set s = 3 and solve for t
$\frac{720}{t} - 2 = 3$
$720 = 5t$
$t =144$