Answer
The jet stream speed is $v_{j} = 88.63 km/h$.
Work Step by Step
We have information on the distance $d = 4350 km$ and the time differences $\Delta t = 50 min$ with longer westward flight than eastward. We have the airplane speed $v_{p} = 966 km/h$ and jet stream speed $v_{j}$ which is presumed to move eastward.
So, we have two different equations: when the airplane flies west,
$d=(v_{p}-v_{j})t_{west}$
and when the airplane flies east,
$d=(v_{p}+v_{j})t_{east}$
Using the information on the time difference, we have:
$\Delta t = t_{west} - t_{east} = \frac{d}{v_{p}-v_{j}} - \frac{d}{v_{p}+v_{j}} = \frac{2dv_{j}}{(v_{p})^{2}-(v_{j})^{2}}= 50 min$
Rearranging the equation, we obtain a quadratic function for $v_{j}$:
$(v_{j})^{2} + 2.4dv_{j} - (v_{p})^{2} = 0$
Substituting the numbers and solving the equation for $v_{j}$, we obtain
$v_{j} = 88.63 km/h$
