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.

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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) About Me  (Show Source):
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r%5Ba%5D, air speed
r%5Bw%5D, wind speed

Then ground speed with a head wind is r%5Ba%5D-r%5Bw%5D and ground speed with a tail wind is r%5Ba%5D%2Br%5Bw%5D

To travel 1000 miles in 4 hours, ground speed must be 1000%2F4=250 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 1000%2F%2810%2F3%29=300 mph.

So:
r%5Ba%5D-r%5Bw%5D=250, and
r%5Ba%5D%2Br%5Bw%5D=300

Add the two equations, term by term:
2r%5Ba%5D%2B0r%5Bw%5D=550

Divide by 2:
r%5Ba%5D=275

Since r%5Ba%5D-r%5Bw%5D=250 and r%5Ba%5D=275,

275-r%5Bw%5D=250
r%5Bw%5D=25

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