Answer
The path that allows us to cross the river in the shortest time is at an angle of $39^{\circ}$ north of east.
Work Step by Step
In order to cross the river in the shortest time possible, we should try to maximize the component of velocity which is directed straight across the river. Therefore we should try to swim straight across the river at a speed of 1.5 m/s to the east.
Because the water is moving north, our velocity will also have a component of 1.2 m/s to the north.
Therefore our optimal path across the river will have an angle of $\theta$ which is north of east.
$tan(\theta) = \frac{1.2}{1.5}$
$\theta = tan^{-1}(\frac{1.2}{1.5}) = 39^{\circ}$
The path that allows us to cross the river in the shortest time is at an angle of $39^{\circ}$ north of east.
