I'm also confused. There is a 5:30PM and 6:59PM departure from DCA to JFK. Which flight is on the OP on. Even the later flight which is scheduled at as an 8:24PM arrival should easily get the OP into JFK for a CX 1AM departure, any delays included. If the OP left his office by 345PM he should get to DCA by 430PM in time to go standby on the 530PM flight (using a cab). It seems as though Amtrak would be a costly alternative and I don't see the OP getting to JFK that way much before 9:30PM.
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This story still makes no sense to me. Ok, you're on the basically 1am departure from JFK on CX i take it. you're willing to spend the bucks on amtrack to Penn Station then you'll have to get all the way out to JFK. Yet, you wouldn't just take a taxi from your office to DCA? that would be far cheaper and less hassle. Just makes no sense.
I'm on:
AA3633 DCA-JFK 5:30pm - 7:00pm
CX0889 JFK-HKG 10:00pm
* CX0845 leaving at 12:50am doesn't operate on required day that connects to the AA flight.
* The earlier AA DCA-JFK flight departs at 12:50pm. I can't leave work that early.
* I can take the Amtrak 4:02pm train out of DC Union Station (which is right across the street from my workplace) and get into New York Penn Station at 7:20pm. Then I can take the 7:47pm LIRR to Jamaica, connect to the Air Train, and arrive T7 by 8:45pm. BTW, I can ride Amtrak for free, for the most part.