Question 606328: Fern can fly her plane 240 miles against the wind in the same time it takes her to fly 360 miles with the wind. The speed of the plane in still air is 30 mph more than 4 times the speed of the wind. Find the speed of the plane in still air.
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! Fern can fly her plane 240 miles against the wind in the same time it takes her to fly 360 miles with the wind. The speed of the plane in still air is 30 mph more than 4 times the speed of the wind. Find the speed of the plane in still air.
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Let v = the speed in still air
Let w = the speed of the wind
The speed with the wind is v + w, the speed against the wind is v - w
Given: v = 4w + 30 [speed in still air is 30 more than 4 times the wind speed]
Solve for w:
w = (v-30)/4
Since time = distance/speed, and the times are the same, we can write
240/(v-w) = 360/(v+w)
Using the expression for w above, we have
240/(v-(v-30)/4) = 360/(v+(v-30)/4)
Simplifying and solving for v gives v = 150 mph
Check: w = (150-30)/4 = 30 mph
240/(150-30) = 360/(150+30)
240/120 = 2
360/180 = 2
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