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It's my understanding that passengers in this game are not smart enough to wait longer for a train that is direct. They will get on a local train that takes them a little closer to their destination even if there is no full connection to their destination and with no regard to efficiency.
In addition even if the above were untrue, the principle is that passengers look for a route less than 1.5x the straight line distance. This means that with only dedicated direct runs you will be picking up passengers bound for Sacramento, Shasta, and maybe even Carson City, depending how direct your route is.
You might be interested in a bit of this video:
https://www.youtube.com/watch?v=FHg6xqXe3dk
What Gnaal may be missing is to use "minimum > 0" and "passengers" only to force trains to wait for passengers before even leaving SLC.
Once passengers have boarded a train they don't care how long the train waits before departing.
If you want to play it using the fewest trains just set the minimum to 8 and only allow passengers to board the first 7 trains and the 8th train to a minimum of 2 passengers. That's 7x 8 + 2 = 58 cars with a total of 58x 35 = 2,030 passengers.
Note that passengers only wait for 14 days (in a 20 year scenario) for a train to pick them up, then they find other transportation (horse drawn wagons, not explicitly shown in the game.) That means to capture *all* the potential passengers, you want to have a train at SLC ready to pick them up at "all" times, and once one leaves the Station there, you need to have another train for them to board within 2 weeks.
Once those passengers are on your train, they become patient and will sit there not moving for months while you load more passengers, so you can set Min 8 carloads to load up a full trainload. Passengers pay more for quicker trips, but the effect is small so you don't really benefit from running more shorter trains in this case, but if you want to watch progress happen, you can run more trains with fewer than 8 carloads of passengers. The downside is that you have to buy more trains and they do take track space, but it's fine if you want to watch the progress rise more steadily.
Another point on long-range routes like this: you should generally prohibit goods that are available nearer the destination. Moving Beer and Meat from far away is expensive and may even prevent deliveries from nearer more profitable locations, so don't allow it unless you have a good reason!
I didn't even do anything clever with the loading, by that I mean that mail was also hauled on those trains. So they weren't always just full of passengers. From memory, I saw that those first 8 got me reasonably close to the target, so much so that after some maths I decided I could just let nature take its course and left the trains to make the subsequent journeys without keeping an eye on them.
Maybe my key factor was setting the trains off 10 days apart.
I had something like 10-20 engines (fast ones, usually only hauling one car each of p+m) on the direct route thinking that would just solve it. But there are some good suggestions here, guess I'll reload into some of my bookmark savefiles for it and try to complete it during Xmas, thanks!