If I remember correctly, the road sign at alexandra arch says 2.4km to mount faber. The 2.4km is definitely not accurate because I took 1hr+ to get to jewel box. I did the walk with my gf starting from hort park because it is a "nice, short 30min walk before lunch" so 9km is probably accurate.
Bring lots of water and expect to walk at least 3-4 hours if you are stopping to take photos. Start around 9am and you will get to vivo on time for lunch.