Question

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?

Answer 1

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