find the speed of the wind.

Question

an airplane flew 660 miles with the wind,and then took 40 minutes longer for the return flight against this wind.if the planes flies 200 miles per hour in still air,find the speed of the wind.

Answer 1

Let x = speed of wind

 

Then, 200 + x = speed of the plane with the wind

           200  - x = speed of the plane against the wind

 

Note that 40 minutes = 2/3 hour

 

Distance = (Rate)(Time), so Time = distance/rate

 

Time with the wind = Time against the wind - 2/3

 

660/(200+x) = 660/(200-x) - 2/3

 

Multiply through by the LCD, 3(200+x)(200-x) to get:

 

1980(200-x) = 1980(200+x) - 2(200+x)(200-x)

 

Divide both sides by 2:  990(200-x) = 990(200+x)-(200+x)(200-x)

 

198000 - 990x = 198000 + 990x -(40000 - x²)

 

-990x = 990x - 40000 + x²

 

So, x² + 1980x - 40000 = 0

 

Using the Quadratic Formula, we have:

 

x = -1980 ± √[1980² - 4(1)(-40000)]

                                2

 

x = -1980 ± √4080400

                  2

 

x = -1980 ± 2020  = 20, -2000

                  2

 

Since the speed of the wind can't be negative, x = 20 MPH