An airplane takes 7 hours to travel a distance of 4707km against the wind. The return trip takes 6 hours with the wind. What is the rate of the plane in still air and what is the rate of the wind?

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Answer 1 · 2018-07-17T09:25:14

The speed of the airplane is #=728.5kmh^-1#. The speed of the wind is #=56.0kmh^-1#

Let the speed of the airplane in still air be #=v_akmh^-2#

Let the speed of the wind be #=v_wkmh^-2#

Thefore,

Then, the on going speed is

#v_a-v_w=4707/7#...................#(1)#

And the return journey is

#v_a+v_w=4707/6#..................#(2)#

Solving equations #(1)# and #(2)#

#2v_a=4707/7+4707/6=4707(1/7+1/6)#

#v_a=728.5kmh^-1#

The speed of the airplane is #=728.5kmh^-1#

And

#2v_w=4707/6-4707/7=4707(1/6-1/7)#

#v_w=56.0kmh^-1#

The speed of the wind is #=56.0kmh^-1#