Flying against the wind, an airplane travels 4620km in 6 hours. flying with the wind, the same plane travels 3750km in 3 hours. what is the rate of the plane in still air and what is the rate of the wind?

Let us call the rate as velocity. Now the velocities of the plane and of the wind are:
and :
Now

case 1:

case 2:

from equation 2:
substitute in equation 1:

Which is your velocity in still air (without wind)
Substituting back in:

you get:

which is the wind velocity