Answer
$5.1\space m/s,\space 51.34^{\circ}\space North\space of\space west$
Work Step by Step
Please see the attached image first.
Let's take,
Neil's velocity relative to Barbara = $V_{NB}$
Neil's velocity relative to Ground = $V_{NG}=3.2\space m/s\leftarrow$
Barbara's velocity relative to Ground = $V_{BG}=4\space m/s\downarrow$
By using the Pythagorean theorem, we can get.
$V_{NB}=\sqrt {V_{NG}^{2}+(-V_{BG})^{2}}=\sqrt {(3.2\space m/s)^{2}+(-4\space m/s)^{2}}=5.1\space m/s$
By using trigonometry, We can get.
$tan\theta=\frac{|V_{BG}|}{|V_{NG}|}=\frac{4\space m/s}{3.2\space m/s}=>\theta=tan^{-1}(1.25)=51.34^{\circ}$ North of west
