Answer:
Speed of the plane in still air: .
Windspeed: .
Step-by-step explanation:
Assume that is the speed of the plane in still air, and that
is the speed of the wind.
- When the plane is travelling against wind, the ground speed of this plane (speed of the plane relative to the ground) would be
.
- When this plane is travelling in the same direction as the wind, the ground speed of this plane would be
.
The question states that when going against the wind (,) the plane travels
in
. Hence,
.
Similarly, since the plane travels in
when travelling in the same direction as the wind (
,)
.
Add the two equations to eliminate . Subtract the second equation from the first to eliminate
. Solve this system of equations for
and
:
and
.
Hence, the speed of this plane in still air would be , whereas the speed of the wind would be
.