Intuition is good at finding what to do and what approach to take. This is finding the new dot in the unknown.
Rational thinking is good at explaining why does it work, then. This is connecting the new dot back to what you already know.
Further, my observations suggest that those two are not mutually exclusive. Intuition and feelings can indeed be based on what you already rationally know. They just operate on the unknown area that your consciousness can't reach yet. Intuition isn't too helpful unless you know something about the problem domain. Similarly, rational thinking can't really warp to anything truly new without intuition: the rational mind per se can only take what is already known and expand it a bit. To do otherwise would be, to the rational mind, well, irrational.
Rational thinking is good at explaining why does it work, then. This is connecting the new dot back to what you already know.
Further, my observations suggest that those two are not mutually exclusive. Intuition and feelings can indeed be based on what you already rationally know. They just operate on the unknown area that your consciousness can't reach yet. Intuition isn't too helpful unless you know something about the problem domain. Similarly, rational thinking can't really warp to anything truly new without intuition: the rational mind per se can only take what is already known and expand it a bit. To do otherwise would be, to the rational mind, well, irrational.