SOLUTION: With a head wind, a plane traveled 1000 mi in 4 h. Withe the same wind as a tail wind, the return trip took 3 h 20 min. Find the plane's air speed and wind speed.

Question 130733This question is from textbook
: With a head wind, a plane traveled 1000 mi in 4 h. Withe the same wind as a tail wind, the return trip took 3 h 20 min. Find the plane's air speed and wind speed. This question is from textbook

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
, air speed
, wind speed

Then ground speed with a head wind is and ground speed with a tail wind is

To travel 1000 miles in 4 hours, ground speed must be mph.

To travel 1000 miles in 3 hours 20 minutes, which is 3 and 1/3 hours, or 10/3 hours, ground speed must be mph.

So:
, and

Add the two equations, term by term:

Divide by 2:

Since and ,

So the air speed is 275, and the wind speed is 25.
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