Answer
302 km, 193$^o$ (i.e., 13$^o$ south of west).
Work Step by Step
Add the displacements using the components method. The two vectors point at 180 degrees and 225 degrees, measured counterclockwise from east.
x-component:
$(225 km)(cos 180^{\circ}) + (98 km)(cos 225 ^{\circ}) = -294.3 km$
y-component:
$(225 km)(sin 180 ^{\circ}) + (98 km)(sin 225 ^{\circ}) = -69.3 km$
Use the Pythagorean theorem 3.4a to find the magnitude of the overall vector, and the definition of tangent, equation 3.4b, to find the angle. The vector has negative x and y-components, and points down and to the left.
