Why was a book that had direct quotes written over 40 years after Jesus died?

Because Matthew, Mark and Luke all use similar (if not identical) words in quoting Christ, it is possible that an earlier source doent of quotes (known as "Q") was used by all three authors. This source doent appears to have been lost. Another possibility is that Mark and Luke are based on Matthew. John was penned later to help consolidate different early church teachings and establishes many of the tenets Christians attribute to Christ, even though they differ in many ways from the doctrine in the earlier gospels.