They're turning into a gold cost in 6.0 anyway.
As far as 'will you get 60'...that's really up to you. It's certainly enough playtime to do it, but most of us here are super veterans of this stuff and can do it REALLY quickly if we want to. It mostly just comes down to efficiency:
Are you spamming dungeons?
If you are, are you a tank?
Are you a healer?
If not, you should be questing hard between queues.
Never do the same dungeon more than once if you can help it, use queue specific when you need to to not outlevel other dungeons, etc.
Even within that confine, how quickly the dungeon goes can rest really heavily on your own shoulders and knowledge of the dungeon if you do tank (which has the fastest queues and by far the most impact on the dungeon, even in terms of DPS these days).
Wait, they're removing Justice/Valor points and replace heirlooms cost to gold in the upcoming patch? If true, I may have to loot more currency later on.