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