Plane traveling in air.

Question

A plane traveling with the wind travels 1300 miles in 5 hours. The return trip is against the wind and takes 13 hours. Find the rate of the plane in still air and the rate of the wind.
plane in still air ____ mph and wind speed ____ mph

Answer 1

Let x = speed of plane in still air and y = speed of the wind

 

Distance = (Rate)(Time)

 

Speed of plane with the wind = x+y

 

Speed of plane against the wind = x-y

 

So, we have the following system of equations:  5(x+y) = 1300

 

                                                                     13(x-y) = 1300

 

5x + 5y = 1300

13x - 13y = 1300

 

Divide the second equation by 13:   5x+5y = 1300

                                                      x - y = 100

 

Multiply the second equation by -5:  5x+5y = 1300

                                                    -5x+5y = -500

 

Add the equations to get 10y = 800

 

                                        y = 80 mph = speed of wind

 

                                        Since x-y=100 and y = 80, we have x = 180 mph = speed of plane without wind