Distance of speed

Question

An airplane take 3 hours to travel a distance of 1950 miles with the wind. The return trip takes 5 hours against the wind. Find the speed of the plane in still air and the speed of the wind.

Answer 1

distance = speed x time

 

let v be the speed of plane

 w be the speed of wind

 when the plane is going with the wind its total speed is v+w,

going against the wind its speed is v-w, so we have

going with the wind:

 

1950=(v+w)(3)

 

650= v+w

 

going against the wind:

 

 

1950=(v-w)(5)

 

390= v-w

 

add these two equations

1040=2v

 

 520=v

subsituting v=520 in v-w=390

 

 

520-w=390

w=130

 

So speed of plane=v=520 mi/hr

speed of wind=w=130 mi/hr