Answer
$794mi/h$, N $26.6^{\circ}$ W
Work Step by Step
Step 1. Recall the wind velocity as $\vec {v_w} =55cos60^{\circ} i + 55sin60^{\circ} j=\frac{55}{2}i+\frac{55\sqrt 3}{2}j$
Step 2. Identify the jet velocity as $\vec {v_j} =765cos120^{\circ} i + 765sin120^{\circ} j=-\frac{765}{2}i+\frac{765\sqrt 3}{2}j$
Step 3. The true velocity of the jet is the sum of the above vectors as $\vec {v_t} =\vec {v_j} +\vec {v_w} =-355i+410\sqrt 3j$
Step 4. The true speed of the jet is the modulus of the velocity: $|\vec {v_t} |=\sqrt {(355)^2+(410\sqrt 3)^2}\approx794mi/h$,
and direction of the jet with respect to the $-x$-axis is $\theta=tan^{-1}\frac{410\sqrt 3}{355}\approx63.4^{\circ}$ or N $26.6^{\circ}$ W
