Whats the speed of the wind? and whats the speed of the plane in still air?

Question

a plane takes two hours to travel 1000 miles with the wind. in the same time, it can travel only 808 miles against the wind.

Answer 1

Here is an algebraic solution:

 

Let x = speed of plane in still air

     y = speed of wind

 

Then x+y = speed of plane with the wind

        x-y = speed of plane against the wind

 

Distance = (Rate)(Time)

 

We have:  2(x+y) = 1000

               2(x-y) = 808

 

So, x+y=500

     x-y=404

 

Add the equations to get 2x = 904

 

                              So, x = 452 mph and y = 48 mph

 

 

Answer 2

While traveling with the wind, the speed of wind adds up to that of the plane in still air and gives resultant speed, which is (1000/2) miles per hour = 500 miles per hour

Thus, while traveling against the wind,  the speed of wind is reduced from that of the plane in still air and gives resultant speed, which is (808/2) miles per hour = 404 miles per hour

Adding up the resultant speeds, we obtain a speed twice that of the plane in still air, which is=(500+404)miles per hour =904 miles per hour 

Thus the speed of the plane in still air is = 904/2 miles per hour = 452 miles per hour 

The speed of the air must be (500-452) miles per hour = 48 miles per hour

Because subtracting this speed of air from speed of the plane in still air we get, (452-48) miles per hour = 404 miles per hour 

 

Hence The speed of the wind is  48 miles per hour and the  speed of the plane in still air is 452 miles per hour.