At least in the case of Chicago(dunno if it's the same in DC), it seems like more and more except in limited cases in recent years at Chicago Union Station, that Amtrak hasn't been holding outbound trains for connecting passengers from other arriving trains to allow them to connect to a different departing train. I wonder if Amtrak sometimes does this in other places where passengers often connect between trains, such as DC and LA? Seems like the exception(per checking on juckins.net ) is Portland, where I notice to a greater extent Amtrak has sometimes held up a departing train 28(Empire Builder eastbound), to allow train 14 passengers(Coast Starlight going north) to connect to that train going east.
Like others said, Amtrak would probably allow you to travel outbound on train 97, if you miss a departing train 91 going out of DC. Reminds me of how for passengers who miss the 30 Capitol Limited departing Chicago and going east, that they allow those passengers if they want to(anyone between Chicago and Cleveland) to ride train 48(Lake Shore Limited) instead. Personally I wish there was a greater window of time between 30's arrival time(1:05pm) and 91's departure(3:05pm), to make me feel easy I'd make this connection on the same day. But that's just my opinion.
I'll allow those who more often travel out of DC, to comment what Amtrak tends to do on how they accommodate passengers from a late train 30 into DC, onto outbound train 91. I would hope they'd provide bussing from a certain Carolinas stop if say one's destination was along train 91(i.e. Columbia, SC), and the passenger had to get off somewhere to catch a bus that'd take them to that other city/town properly. I.e. passenger got off at Florence, and a bus ran that'd take those passenger(s) from Florence Amtrak station west to Columbia. Who knows if such bus service exists, myself?
