How did the Nazgul reach the Shire Before Gandalf?

[Morgoth the Great]

we all know that Gandlaf was carried by Gwaihir to Edoras, and he then took Shadowfax, fastest of all horses. He then surely went directly to The Shire, knowing that the Nazgul were going there. The Nazgul however, dont know where the shire is, and have to rely on directions from Grima Wormtongue. He directs them a way that sends them past the Rangers. They also dont really know where they are going, and would therefore be slowed a bit more than Gandalf, who knows exactly where he is going. Gandalf however, despite being on a faster horse, with a headstart(he must of been going faster than Grima was, and therefore was nearer to the Shire) unthwarted, and with a much clearer sense of direction still managed to "lose the race" with the Nazgul, and the Ringwraiths got to the Shire first. can anyone clear this up for me(or indeed begin a debate)??