Question

A plane is going to fly 300 miles at a planned speed of 530 mph. The flight will have an average

headwind of w miles per hour the entire time, meaning the plane is flying directly against the
wind. The time T, in hours, of the flight is a function of the speed of the headwind w, in mph, and
can be modeled by
T(W) =
Here is the graph of y = T(w):
7 (travel time)
10
8
4
2
300
530-W
a.
100
500
200
300
400
w (headwind speed)
What does T (110) mean in this situation?
600
b. At what value of w does the graph have a vertical asymptote? Explain how you know a
what this asymptote means in the situation.

Answer 1

T(110) represents the time it takes for the plane to fly 300 miles against the headwind, which has a speed of 110 mph. It is approximately 0.7143 hours or 42.857 minutes.

Step-by-step explanation:

T(110) represents the time it takes for the plane to fly 300 miles against the headwind, which has a speed of 110 mph. It can be calculated using the given function:

T(w) = 300 / (530 - w)

Substitute w = 110 into the function:

T(110) = 300 / (530 - 110) = 300 / 420 = 0.7143 hours

Convert the time to minutes:

0.7143 hours * 60 minutes/hour = 42.857 minutes

Therefore, T(110) means the flight will take approximately 0.7143 hours or 42.857 minutes.