Let us call the rate as velocity. Now the velocities of the plane and of the wind are:
[tex] v_{p}[/tex] and [tex] v_{w} [/tex]:
Now
case 1: [tex] v_{p} - v_{w} =4620/6=770 km/h[/tex]
case 2: [tex] v_{p} + v_{w} =3750/3=1250 km/h [/tex]
from equation 2: [tex] v_{w} = 1250 - v_{p} [/tex]
substitute in equation 1:
[tex]v_{p} - 1250 + v_{p} =770 v_{p} = 1010 km/h [/tex]
Which is your velocity in still air (without wind)
Substituting back in:
[tex] v_{w} = 1250 - v_{p} [/tex]
you get:
[tex] v_{w} = 1250-1010 = 240 km/h [/tex]
which is the wind velocity