Plane speed need help /:

Question

A plane traveled 460mph with the wind and 400 mph against the wind. Find the speed of the plane in still air and the speed of the wind. 

Answer 1

let say X is the wind speed  and Y is the plane speed in still air

 

 

460 = Y +X

400 = Y - X

 

use elimination method (add both equations)

 

860 = 2Y

 

Y = 430 mph

 

plug in Y = 430

 

460 = 430 + X

 

X= 30 mph

 

Answer 2

Cool so we can come up with two equations based on each scenario

 

the first scenario we have the wind working in our favor so

 

S_a + w = 460

 

the second case the wind is against us thus

 

S_a - w = 400

 

Now simply solve the system of equations I'm going to use elimination to get rid of w 

 

Simply add the two equations

 

2S_a = 860

 

S_a = 860/2 

 

= 430 mph

 

 

That's t the speed of the aircraft in still air and the speed of the wind would be found by using any of the two equations 

 

w = 430 - 400 

 

= 30 mph

 

those are the two answers to your question.