SOLUTION: A plane has a cruising speed of 200 miles per hour when there is no wind. At this speed, the plane flew 500 miles with the wind in the same amount of time it flew 300 miles against

Question 950040: A plane has a cruising speed of 200 miles per hour when there is no wind. At this speed, the plane flew 500 miles with the wind in the same amount of time it flew 300 miles against the wind. Find the speed of the wind.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A plane has a cruising speed of 200 miles per hour when there is no wind. At this speed, the plane flew 500 miles with the wind in the same amount of time it flew 300 miles against the wind. Find the speed of the wind.
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a = the plane's airspeed = 200 mi/hr
w = windspeed
---
d = r*t
t = d/r
Going upwind (against the wind) the groundspeed = 200 - w
Going downwind (with the wind) the groundspeed = 200 + w
---
t = 500/(200+w) = 300/(200-w)
500*(200-w) = 300*(200+w)
5*(200-w) = 3*(200+w)
1000 - 5w = 600 + 3w
8w = 400
w = 50 mi/hr

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