Answer
$\text{Average airspeed of the plane is 175 mph}$ and
$\text{Average wind speed is 25 mph.}$
Work Step by Step
Let us consider that $\text{x=airspeed of the plane, and}$ $\text{y = wind speed}$
We are given that the total speed is $(x+y)$ with a tail wind,
$3(x+y)=600~~~~(1) $
and the total speed is $(x-y)$ against the wind,
$4(x-y)=600~~~~(2)$
Equation (1) and (2) can be re-written as:
$(x+y)=200~~~~(3) $
and
$(x-y)=150~~~~(4)$
We add equations (3) and (4) to obtain:
$2x=350 \implies x=175$
Now, back substitute the value of $x$ into Equation (3) to solve for $y$:
$y=200-175=25$
Therefore, our desired results are:
$\text{Average airspeed of the plane is 175 mph}$ and
$\text{Average wind speed is 25 mph.}$
