Having practically sprinted off the plane, we (my new friend and I!) found a very helpful lady in arrivals who cheerfully told us we had almost certainly missed our connection and handed us each a piece of paper containing the hotel reservations which had been made on our behalf, and the time of the alternative flight tomorrow. Great. In small print at the bottom of the page it said, somewhat sardonically, "If you do wish to try and make your flight, go to gate D39". So we hurried through customs with as much agitated urgency as it was possible to convey without seriously pissing off some edgy American officials and hurried on to Gate D39 just in time to join the queue boarding the plane.