- They moved farther down the road.
- They moved further down the road.
Farther and further have the same meaning and both are correct. Further is more commonly used.
Further is used in metaphorical and more abstract contexts, especially when referring to time:
- We are going to stay here for a further 3 days.
- Do you have any further comments?
- I would like to start the meeting without further delay.
The same approach applies for farthest and furthest.
- It is the farthest station from my house.
- It is the furthest station from my house.
- Team ‘A’ has moved furthest with the project.