I’ve run into this dilemma in some of my own work as well as the work of others out there. This pair of words is one of the trickier to get right because, for a time, they were interchangeable. Both can mean a more distant point, or to a greater extent or degree. So, which one is which?
Somewhere many moons ago, someone got the great idea to distinguish between the two words rather than allow the interchangeability to continue. Who knows? It could have led to some catastrophic war. Anyway, the difference in the use of these two words is described below:
farther — this word should be reserved to denote physical differences or degrees.
further — this word should be reserved to denote non-physical or metaphorical advancement or change.
Or you may choose to remember it this way: Going further, if you can throw your ball farther than mine, then I’ll buy you an ice cream.
Hope this helps.