A plane travels from Orlando to Denver and back again. On the five-hour trip from Orlando to Denver, the plane has a tailwind of 40 miles per hour. On the return trip from Denver to Orlando, the plane faces a headwind of 40 miles per hour. This trip takes six hours. What is the speed of the airplane in still air?

Question

A plane travels from Orlando to Denver and back again. On the five-hour trip from Orlando to Denver, the plane has a tailwind of 40 miles per hour.  On the return trip from Denver to Orlando, the plane faces a headwind of 40 miles per hour. This trip takes six hours. What is the speed of the airplane in still air?

mathstudent55 · Answer

Let the speed of the plane in still air = x
When there is a tailwind, the speed is x + 40
When tere is a headwind, the speed is x - 40

speed = distance/time, or
s = d/t
distance = speed * time, or
d = st

Orlando to Denver
d = st = (x + 40)5

Denver to Orlando
d = st = (x - 40)6

The distance is the same both ways, so
(x + 40)5 = (x - 40)6

Solve the equation for x.