What is the plane's speed in still air?

Question

7. A plane flies 600 miles with a tail wind in 2 hours. It takes the same plane 4 hours to fly the 600 miles when flying against the wind. What is the plane's speed in still air? 

 

Answer 1

With the tail wind the effective speed is aided by the wind:

 

v + u = 600/2 = 300 mph

 

 

With the head wind, the effective speed is lowered:

 

v - u = 600/4 = 150 mph

 

 

 

From the two equations, 2v = 450, so v = 225 mph in still air.

 

u = 75 mph for the speed of the wind.

Answer 2

Rate * time = Distance

r + w * 2    = 600

r - w  * 4    = 600

 

2r + 2w = 600

4r - 4w = 600

 

4r + 4w = 1200

4r - 4w  =  600

 

8r          = 1800

r            =  225

 

2(225) + 2w = 600

2w                 = 150

w                   =  75

 

So the plane is travelling at 225 mph with a wind of 75. With the wind this becomes 300 mph and takes 2 hours. Against the wind it is traveling  at 150 and takes 4 hours.

No wind, it would travel at 225 mph.