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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 :

Giovi
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



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