FARTHER and FURTHER both mean “at a greater distance,” and they often are used interchangeably in this sense — but they are not quite the same. Let’s take a look:

FARTHER typically refers to physical length or distance. It is the comparative form of the word “far” when referring to distance.

FURTHER typically refers to abstract distance. It can also mean “to a greater degree,” or “additional.” It refers to time or amount.

Correct: London is farther north than Juneau. (Refers to physical distance)
Correct: This plan requires further study. (Meaning “additional,” refers to amount)
Correct: According to my timetable, we should be further along. (Refers to time)

TIP:
Use FARTHER for physical distance and FURTHER for abstract/metaphorical distance.
FARther has FAR in it, and “far” relates to physical distance.