SOLUTION: Without any wind an airplane flies at 200 mph the plane travels 800 miles into the wind and then returns with the wind in the total time of 10 hours Find the average speed of the

Question 1027099: Without any wind an airplane flies at 200 mph the plane travels 800 miles into the wind and then returns with the wind in the total time of 10 hours Find the average speed of the wind
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Time against wind is 800/(200-w)
Time with wind is 800/(200+w)
the units help--top is miles divided by miles/hr, so the final units are hr.
(800/(200+w))+(800/(200-w))=10
Divide everything by 10.
(80/(200+w))+(80/(200-w))=1
multiply by (200+w)(200-w)
80(200-w)+80(200+w)=40000-w^2 (internal products cancel)
32000=40,000-w^2, because the 80(-w)+80(w) cancel
w^2=8000
w=89.44 mph.
Check
on trip out, speed is 111.56 mph or 7.236 hours (here, I don't round until the end)
on way back, speed is 289.44 mph or 2.763 hours.
The exact value is 40 sqrt(5) mph
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