Answer
Average airspeed of the Piper is 175 mph.
Average wind speed is 25 mph.
Work Step by Step
Let
x = airspeed of the Piper,
y = wind speed.
With a tail wind, total speed is (x+y), $3(x+y)=600\qquad(1)$
Against the wind, total speed is (x-y), $4(x-y)=600\qquad(2)$
Divide the equations with 3 and 4, respectively
$\left\{\begin{array}{ll}
x+y & =200\\
x-y & =150
\end{array}\right.$
Adding,
$2x=350$
$x=175$
Back-substituting,
$175+y=200$
$y=25$
Average airspeed of the Piper is 175 mph
Average wind speed is 25 mph.
