Assume the speed of the plane is u and that of wind is v

Therefore, u+v = 470 mile ..... (1) (since the plane can travel 470 mile with the wind)

and u-v = 390 ...........(2) (since plane can travel 390 mile against air)

adding eqn 1 and 2, 2u= 390+470 = 860

or u = 430

putting the value of u in eqn 1,

430+v = 470

or v = 470-440 = 30

Answer, Speed of the plane without the wind is 430 mile/hr and speed of the wind is 30 mile/hr