"Farther away" means at a greater physical distance from a point than something else. It compares locations and implies you must travel more to reach it, while further can be abstract.
Men rush to California and Australia as if the true gold were to be found in that direction but that is to go to the very opposite extreme to where it lies. They go prospecting farther and farther away from the true lead, and are most unfortunate when they think themselves most successful. Henry David Thoreau
There are two ways of extending life: firstly by moving the two points "born" and "died" farther away from one another... The other method is to go more slowly and leave the two points wherever God wills they should be, and this method is for the philosophers. Georg Christoph Lichtenberg
Suffering pulls us farther away from other human beings. It builds a wall made of cries and contempt to separate us. Elie Wiesel
The Earth reminded us of a Christmas tree ornament hanging in the blackness of space. As we got farther and farther away it diminished in size. Finally it shrank to the size of a marble, the most beautiful marble you can imagine. James Irwin
What you've done is done. You've got a goal you never reach, and it's always farther away. It keeps you walking. I don't want to sit down. Christopher Lambert
Notoriety travels farther away. Chinese Proverb