SOLUTION: A plane can fly 259 miles downwind in the same amount of time as it can travel 161 miles upwind. Find the velocity of the wind, v, if the plane can fly 210 mph in still air.
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Question 316576: A plane can fly 259 miles downwind in the same amount of time as it can travel 161 miles upwind. Find the velocity of the wind, v, if the plane can fly 210 mph in still air. Found 2 solutions by texttutoring, solver91311:Answer by texttutoring(324) (Show Source):
You can put this solution on YOUR website! If you're going downwind, you add the wind's velocity (vw) to the plane's still air velocity:
Downwind: v = 210+vw
If you're going upwind, you have to subtract the wind's velocity:
Upwind: v = 210-vw
Now use the formula D=VT, where D=distance, v=velocity, and t=time. We know that the times are the same, so isolate for t and set them equal to each other:
Which can (more conveniently for this problem) be expressed as:
When the plane flies against the wind, the actual speed is the speed in still air MINUS the speed of the wind. With the wind, speed in still air PLUS wind speed.
Having two expressions equal to the elapsed time, , regardless of how long that might be, we can set them equal to each other, eliminating time of flight as a factor in the calculation.
Now all that is left is to cross multiply and solve for .