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

i really don't understand this, please help

Answer 2

For part 1, use the given hint.
\[d=rt\]
notice that we have \(d=720\) here, so
\[720=rt \implies r = \dfrac{720}{t}\]

Answer 3

`The pilot's final score s is the average speed minus any penalty points p earned.`

\[s = r - p\]

plugin the value of \(r\) above

Answer 4

\[s=\dfrac{720}{t}-p\]

thats the function for part1

Answer 5

ok thank you, I actually already understood that part

Answer 6

it's number 2 i need help with

Answer 7

good, for part2, simply plugin \(p=2\) and graph the function

Answer 8

oh, yeah of course

Answer 9

so for part 3 do I just look for the maximum point on the graph?

Answer 10

nope, for part3, simply plugin \(s=3\) in the function and solve \(t\)

Answer 11

\[3=\dfrac{720}{t}-2\]

solve \(t\)

Answer 12

t=144

Answer 13

so that's the maximum time

Answer 14

Yes thats the maximum time acceptable

anything greater than that will reduce the score

Answer 15

ok, thanks again!

Answer 16

yw