If my logic is correct, the answer is 1.5707~ times the speed of the man, or pi/2 times his speed.
Reasoning: We have a square area of length n metres to a side.
|G----|
|R |
| |
| |
|M G
|-----|
The ram is in the top left corner represented by the R symbol, and the man is in the bottom left corner, represented by the M symbol. Assuming the ram does not pursue the man directly, but instead heads straight for the gate, we find that the lower bound for the ram's speed to reach the gate at the same time as the man to be sqrt(2) times the man's speed using pythagoras' theorem.
This is not the case, however, and the ram is constantly charging the man, adjusting his direction as the man moves. This means the ram's path will be curved, and the final path drawn after both have moved to the gate will be a quarter circle assuming they both reach the gate at the same time.
From there, it's a simple case of calculating the length of a quarter circle (2pi*r / 4) = pi*r / 2. Since we can assume the length of each side of the area to be 1, that works out to pi/2. If the ram moves at pi/2 times the man's speed, he will catch the man at the gate. If the ram moves faster, the path will be straighter and he will catch the man before he escapes. If the ram moves slower, he will miss the man entirely.