SOLUTION: The helicopter could fly at 4 times the speed of the wind. Thus, it could travel 600 miles downwind in 1 hour more than it took to travel 300 miles upwind. What was the speed of th

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Question 1030170: The helicopter could fly at 4 times the speed of the wind. Thus, it could travel 600 miles downwind in 1 hour more than it took to travel 300 miles upwind. What was the speed of the helicopter in still air?
---I am not sure how this problem is solved. I have done other problems somewhat similar to this, but this is a bit more difficult. An explanation would be greatly appreciated. Thank you!
Found 2 solutions by stanbon, MathTherapy:
Answer by stanbon(75887) About Me  (Show Source):
Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
The helicopter could fly at 4 times the speed of the wind. Thus, it could travel 600 miles downwind in 1 hour more than it took to travel 300 miles upwind. What was the speed of the helicopter in still air?
---I am not sure how this problem is solved. I have done other problems somewhat similar to this, but this is a bit more difficult. An explanation would be greatly appreciated. Thank you!
Let the speed of the helicopter, in still air, be S

Then speed of wind = matrix%281%2C3%2C+%281%2F4%29S%2C+or%2C+S%2F4%29

Time it took to travel downwind: 600%2F%28S+%2B+S%2F4%29

Time it took to travel upwind: 300%2F%28S+-+S%2F4%29 

We then get: 600%2F%28S+%2B+S%2F4%29+=+300%2F%28S+-+S%2F4%29+%2B+1

600%28S+-+S%2F4%29+=+300%28S+%2B+S%2F4%29+%2B+1%28S+%2B+S%2F4%29%28S+-+S%2F4%29 ----- Multiplying by LCD, %28S+%2B+S%2F4%29%28S+-+S%2F4%29

600S+-+150S+=+300S+%2B+75S+%2B+S%5E2+-+S%5E2%2F16

450S+=+375S+%2B+S%5E2+-+S%5E2%2F16 

S%5E2+-+S%5E2%2F16+%2B+375S+-+450S+=+0

S%5E2+-+S%5E2%2F16+-+75S+=+0

16S%5E2+-+S%5E2+-+16%2875S%29+=+0 ------- Multiplying by LCD, 16

15S%5E2+-+16%2875S%29+=+0

15%28S%5E2%29+-+15%285S%29%2816%29+=+0

S%5E2+-+80S+=+0

S(S - 80) = 0

S or speed or helicopter, in still air = highlight_green%28matrix%281%2C2%2C+80%2C+mph%29%29	   OR	      S = 0 (ignore)