SOLUTION: An airplane flies 250 km against the wind and 680 km with the wind in a total time of 4 hour. The speed of the airplane is 300 km/h. What is the speed of the wind?

Question 1031838: An airplane flies 250 km against the wind and 680 km with the wind in a total time of 4 hour. The speed of the airplane is 300 km/h. What is the speed of the wind?
Found 2 solutions by LinnW, Alan3354:
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
Set w = the wind speed.
The time t1 for the 250 km leg is the distance 250 / the speed (300 - w)
The time t2 for the 680 km leg is the distance 680 / the speed (300 + w)
t1 + t2 = 4 hours

w = 205.86 is the wind speed.
Solving completely by hand is fairly tedious.
I used www.wolframalpha.com with the above equation.
If your instructor needs a more detailed solution,
let me know.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
An airplane flies 250 km against the wind and 680 km with the wind in a total time of 4 hour. The speed of the airplane is 300 km/h. What is the speed of the wind?
--------------
a = plane's airspeed = 300
w = windspeed
----
250/(300-w) + 680/(300+w) = 4
250*(300+w) + 680*(300-w) = 4*(300+w)*(300-w) = 360000 - 4w^2
75000 + 204000 - 430w = 360000 - 4w^2
4w^2 - 430w - 81000 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1480900 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 205.865293445465, -98.3652934454652. Here's your graph:

=====================
w =~ 206 km/hr
======================
No fun flying upwind like that.
Downwind is great.
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