If a plane can travel 460 miles per hour with the wind and 040 miles per hour against the wind, find the speed of the plane in still air.

Question

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Answer 1

Let velP = velocity of plane in still air

     velW = velocity  of wind

 

 velocity of plane with the wind = velP + velW = 460 mph     or   velP = 460 - velW

 

 velocity of plane against the wind = velP - velW = 40 mph

 

substituting top equation into bottom equation and solving for velW:

 

460 - velW - velW = 40      (combine like terms)

 

460 - 40 = 2*velW

 

or rearrange  2*velW = 460 -40 = 420

 

velW = 420/2 = 210 mph

 

velP = 460 - velW = 460 - 210 = 250 mph velocity of plane in still air