Let's begin by listing out the information given to us:
velocity (with wind) = 396 km/h
velocity (against wind) = 350 km/h
We will solve by developing a set of equations from the question. Let the velocity of the Plane be represented as p and the velocity of the Wind be represented as w, we have:
![\begin{gathered} p+w=396----1 \\ p-w=359----2 \\ \text{Add equations 1 \& 2, we have:} \\ p+w+p-w=396+359 \\ 2p=755 \\ p=(755)/(2)=377(1)/(2) \\ p=377.5\operatorname{km}\text{/h} \\ Substitute\text{ the value of p into equation 1, we have:} \\ 377.5+w=396 \\ w=396-377.5=18.5 \\ w=18.5\operatorname{km}\text{/h} \end{gathered}]()
Therefore, the speed of the wind is 18.5 km/h and the speed of the plane in still air is 377.5 km/h