Speed and wind speed

Question

An airplane takes 3 hours to travel a distance of 1800 miles with the wind. The return trip takes 5 hours against the wind.  Find the speed of the plane in still air and the speed of the wind.  

Answer 1

Let x = speed of plane in still air

     y = speed of wind

 

Speed of plane with the wind = x+y

Speed of plane against the wind = x-y

 

Distance = (Rate)(Time)

 

Then, 3(x+y) = 1800

         5(x-y) = 1800

 

So, x+y = 600

     x-y = 360

 

Add the equations to get 2x = 960

 

                                     x = 480 mph

                                     y = 120 mph

 

The speed of the plane in still air is 480 mph and the speed of the wind is 120 mph.