The word farther is used for distances:
▶️ I ran 3 miles, but my sister ran 5 miles. She ran 2 miles farther than me.
▶️ Philadelphia is just a two-hour drive away, but Washington is farther – it
takes about 5 hours to get there.
You can remember it because farther has the word “far” in it – which refers to
physical distance.
The word further is used for metaphorical distance – such as time or progress – to
mean “additional” or “to a greater extent.”
▶️ He interrupted me before I could say anything further.
▶️ In order for the research to proceed further, we need more funding.
▶️ We’ve waited long enough; we need to publish this article without further
delay.
However, the dictionary does say that further can also be used for physical
distance:
▶️ There’s a gas station about ten miles farther/further down the road.
Finally, the word furthermore means “in addition” and is used to introduce a
phrase:
▶️ I don’t recommend that school. It’s expensive and the teachers are not very
good. Furthermore, it has neither a library nor a computer lab.
The word furthermore is a bit formal, and when speaking everyday English we
would usually say “Plus” or “Also” instead.