SOLUTION: A plane flew for 576 miles directly into a strong wind and then flew back with the same wind. If the total flying time was 5 hours, and the plane's airspeed was 250 mph, what was

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Question 246104: A plane flew for 576 miles directly into a strong wind and then flew back with the same wind. If the total flying time was 5 hours, and the plane's airspeed was 250 mph, what was the speed of the wind?
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = air speed
250+x = speed with the wind
250-x= speed against the wind

Distance with the wind = Distance against the wind=576
R%2AT%5Bwith%5D=576
T%5Bwith%5D=576%2F%28250%2Bx%29


R%2AT%5Bagainst%5D=576
T%5Bagainst%5D=576%2F%28250-x%29

TOTAL TIME = 5
576%2F%28250%2Bx%29%2B576%2F%28250-x%29=5

Multiply both sides by (250-x)(250+x):
576%28250-x%29%2B576%28250%2Bx%29=5%28250-x%29%28250%2Bx%29
576%2A250-576x%2B576%2A250%2B576x=5%2862500-x%5E2%29
(I'm on vacation, and I don't have my calculator. Use it if you have one!!)

2%2A576%2A250=312500-5x%5E2
576%2A500=312500-5x%5E2
288000=312500-5x%5E2
5x%5E2=312500-288000
5x%5E2=24500
x%5E2+=4900

x=+sqrt%284900%29, which I can do even WITHOUT a calculator!!!

x=+70+ mph--a pretty strong wind!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus