Farther vs Further

One common grammar mistake I've seen is the use of farther vs. further. It seems to be tricky to figure out which word to use in certain situations. The AP style guide clears up the differences in the two.

Farther is referring to physical distance.
     Examples:
                         I can run farther now that I have lost weight.
                         I want to move farther away from the city.

Further is referring to an extension of time or degree.
     Examples:
                          If we are still having issues with connectivity, I will look further into
                          network settings.
                          Nothing could be further from the truth.