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?

Answer 1

Start with knowing that\[Speed*time=distance\]Now let's adjust the speed parts accounting for the wind in both directions. Let s=speed, d=distance, t=time and w=wind:

With tailwind:\[(s+w)*t=d\]With headwind:
\[(s-w)*t=d\]Since the distance traveled in both directions must be the same you can equate the above equations:
\[(s+w)*t=(s-w)*t\]\[(s+40)*5hr=(s-w)*6hr\]Solving for s you should get 440mph which will be the speed without a head or tail wind.