Yes you can travel from SLC to NJ, via Amtrak. You'd take the California Zephyr to Chicago, then transfer to the Capitol Limited to Pittsburgh, and then the Pennsylvanian train east into either one of Amtrak's NJ stops past Philly. Or if you wanted to, could switch to a local commuter train out of Philly, like NJ Transit. It'd take something like 3 days to get to Philly, but it can be done. I like train travel more than flying IMO, and if you don't mind that it'd take 3 days to do, it'd probably be fun to either go one way (or both, up to you) or round trip via Amtrak! Just be advised that Amtrak trains are at times subject to freight train delays, and for all I know your trip has a limited percent chance of taking longer than the train schedules. I'd advise looking up juckins.net to look up archieved average Amtrak arrival times and train delays for each of these 3 trains (#6 in SLC, #6 arriving in CHI, #30 in CHI, #30 in PGH, #42 in PGH), before you travel.
the zephyr will take you to chicago, you can transfer to the capitol limited which will take you to trenton or newark. but the whole trip and experience will suck. amtrak is garbage. honestly you could likely fly there for close to the same price.
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