While the words are related and synonymous in many contexts, they don't quite mean the same thing in all situations.
For example, a slow cat can have quick reflexes.
One person on Yahoo Answers wrote:
I like quick cars but not necessarily fast.
I would take this to mean the writer enjoys a car that can move quickly out of an intersection, but doesn't necessarily cruise at a high speed on the autobahn.
Had the writer said, "I like fast cars but not necessarily quick," then I would assume they would want a car that could easily travel 200 kph on the expressway, but wouldn't care if it's a little sluggish getting started at a red light.
Also, some adjectives simply get associated with certain nouns more than others. And sometimes synonymous words get paired together for emphasis. In a sentence like the one you quoted, for example:
"Relief workers need to be quick and fast," he said.
The speaker is conveying a sense of urgency, and not necessarily expecting anyone to parse those two words carefully, and discern some subtle difference between two.
fast
is used especially for things that move at great speed (not "used only");quick
is more often used to describe something done in a short time (not "exclusively used"). – J.R.♦ Nov 8 '18 at 15:02