Answer
The speed of the falling rain is the same as the speed of the automobile.
Work Step by Step
The parallelogram rule is discussed on pages 28-29, and relative velocity is discussed on page 51.
The rain's velocity relative to the automobile equals the vector sum of its velocity relative to the ground, and the ground's velocity relative to the automobile. These latter two velocities are at right angles.
Because the rain's velocity relative to the car is at 45°, the rain's velocity relative to the ground and the ground's velocity relative to the car must have equal magnitudes.