SOLUTION: A plane can fly 280 miles downwind in the same amount of time as it can travel 190 miles upwind. Find the velocity of the wind if the plane can fly 235 mph in still air.

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Question 1060103: A plane can fly 280 miles downwind in the same amount of time as it can travel 190 miles upwind. Find the velocity of the wind if the plane can fly 235 mph in still air.
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52802)   (Show Source): You can put this solution on YOUR website!
.
A plane can fly 280 miles downwind in the same amount of time as it can travel 190 miles upwind.
Find the velocity of the wind if the plane can fly 235 mph in still air.
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Let "v" be the velocity of the wind under the question, in mph.

Then the speed of the plane flying with    the wind is (235+v) mph, while 
     the speed of the plane flying against the wind is (235-v) mph.

The time spent flying 280 miles with    the wind is  hours.
The time spent flying 190 miles against the wind is  hours.

According to the condition, the times are the same, which gives you an equation

 = .

The set up is done and my work as a tutor formally is completed.

But I will show you how to get your final answer.

Multiply the equation by (235-v)*(235+v). You ill get

280*(235-v) = 190*(235+v),

280*235 - 280v = 190*235 + 190v,

280*235 - 190*235 = 190v + 280v,

21150 = 470v  --->  v =  = 45.


Answer.  The speed of the wind is 45 mph.


Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

A plane can fly 280 miles downwind in the same amount of time as it can travel 190 miles upwind. Find the velocity of the wind if the plane can fly 235 mph in still air.
Let the wind speed be W

Then time spent flying downwind = 

Time spent flying upwind = 

We then get the following TIME equation: 

190(235 + W) = 280(235 - W) ------ Cross-multiplying

190(235) + 190W = 280(235) - 280W

190W + 280W = 280(235) - 190(235)

470W = 90(235)

W, or speed of wind =  

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