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If a plane can travel 480 miles per hour with the wind and 400 miles per hour against the wind, find the speed of the plane in still air
 
 
80 miles per hour? 
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2 Answers

Hello Mishonta.
 
Vivian's generous reply is very correct. I would just like to show you the way I would set up the solution. I like to use descriptive variable names. And I like to take lot's of paper space to setup these things. Even at the risk of looking repetitious. I encourage all my students to be work in this way. It either cuts down on dumb mistakes, or else it makes mistakes easier to track down.
 
Sp = still air Speed of the plane
Sw = the Speed of the wind
 
Sp + Sw = 480  ... in this case the wind speeds it up.
Sp  - Sw = 400  ... in this case the wind slows it down.
 
We can solve for one of the unknowns, by adding the equations:
 
    Sp + Sw = 480
+ (Sp - Sw = 400)
-----------------
  2Sp  + 0 = 880
 
Sp = 880/2
Sp = 440
 
You can use this value in either equation, above, to find that the wind Speed, Sw, is 40.
 
Cheers!
Hi Mishonta;
x=still air speed
wind must be 40 miles/hour because the difference between 480 and 400 is 80, divided by 2 this is 40.
x-40=480
x+40=400
still air speed is 440 miles/hour