Abduction

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Nathan Harper (Taylor Lautner) is an 18-year-old high school senior living in the suburbs of Pittsburgh, Pennsylvania with his parents Kevin (Jason Isaacs) and Mara (Maria Bello). He has been troubled by recurring nightmares and has been seeing psychiatrist Dr. Geraldine "Geri" Bennett (Sigourney Weaver) to diagnose them.
Nathan is teamed with Karen Murphy (Lily Collins) for a school research project on missing children. Nathan discovers he looks very much like an age-progression photo of a missing child, Steven Price. He investigates further and finds other clues that suggest his parents are not his real mom and dad. When he approaches Mara about this, she reveals that she is not his real mother. She goes off crying to get his father to help her explain it all to him.
Two men claiming to be from the Department of Juvenile Justice arrive at Nathan's home in the evening while Mara is on her way to get Kevin. Mara is suspicious and attacks the two, but is shot and killed by the intruders. Kevin is also killed, but not before subduing one agent, as well as yelling for Nathan to run. Nathan runs but returns for Karen, who is now captured by the remaining agent. Nathan overpowers the agent and rescues Karen, he attempts to find out who the man is, but is suddenly forced out of the house because a bomb planted there is about to detonate.
The blast injures Karen, so Nathan takes her to the hospital and attempts to contact the police. His call is intercepted by CIA operative Frank Burton (Alfred Molina) who tells Nathan he is in danger and will send two men to collect him. Nathan is suspicious and while he is trying to make sense of it all, Dr. Bennett appears and helps him and Karen to escape. While driving away, Dr. Bennett explains that Nathan's biological father Martin (Dermot Mulroney) stole an encrypted list of 25 corrupt CIA operatives from the Serbian terrorist Nikola Kozlow (Michael Nyqvist): Kozlow now plans on abducting Nathan to coerce Martin to hand over the list. Nathan had been given to his adoptive parents to protect him. Kozlow used the website to claim Nathan as the missing child Steven Price in order to find him. Dr. Bennett gives Nathan the address of a safe house in Arlington, Virginia and tells him to trust only his biological father Martin and a man named Paul Rasmus. Kozlow's men follow them, but Bennett is able to help them escape. Meanwhile, Burton is warned by his superior to end the situation as soon as possible once he learns of the involvement of Bennett, who is revealed to be a former CIA operative.
Arriving at the safehouse: the two obtain money, a gun, a photo of Nathan's biological mother Lorna Price (Elisabeth RÃ¶hm), and a cell phone. Karen tries to call her family, but her call is intercepted by Burton and the CIA forcing them to flee. Finding the address for his mother, the pair discover the address is a cemetery and that Lorna has died. Nathan and Karen visit her grave and find fresh flowers there, which according to the graveyard attendant, the sender is Paul Rasmus who lives in Nebraska. The two take an Amtrak passenger train to get there using fake IDs provided by their friend Gilly (Denzel Whitaker). En route they confess their feelings for each other and share a passionate kiss. They are unaware that they are followed by Kozlow's right-hand man who abducts Karen when she goes out for food. He leaves her bound and gagged with duct tape in a separate room, but she frees herself by using a piece of broken glass. Nathan fights the right-hand man and he throws him out the window. After the train stops the two make a run for it. Burton's team finds Kozlow's henchman and tracks them down.
Burton explains the data that Martin had stolen and Nathan realizes that the phone from the safehouse contains that data and he surmises that Burton's name is on that list. As Burton tries to play that off, the agents are attacked by Kozlow's snipers. Nathan and Karen take off in a car before they can be caught. As they flee, the cell phone from Kozlow's man rings, the caller is Kozlow and he threatens to kill Karen's parents if Nathan does not hand over the data. Nathan gets Kozlow to agree to make the transaction at a Pittsburgh Pirates baseball game at their home stadium, the PNC Park.
Nathan works with Gilly to obtain tickets and secures a gun to one of the seats with the intent to kill Kozlow. Martin calls Nathan and warns him off, but Nathan refuses to listen. When Kozlow arrives, Karen takes Kozlow's photo so Nathan can recognize him. The two meet and Kozlow tells Nathan how he killed his mother when Nathan was 3 after she refused to give up Martin's location. Kozlow grabs the gun from Nathan and demands the list, Nathan bolts and Kozlow gives chase, followed by CIA operatives who have seen them in the crowd. Nathan is able to escape and Kozlow is killed by Martin. Burton, his superior and his agents arrive. Burton asks for the cell phone, promising to give the decrypted results to his superior. However, Martin had warned his superior about Burton's corruption and takes the phone himself while Burton is taken into custody. Martin calls Nathan, apologizing for not being the father he should have been, Nathan asks him to show himself but Martin refuses. Bennett arrives with Karen and says she has arranged for Nathan to live with her until he decides what to pursue in his life. As the movie ends, Nathan and Karen go on a date in the empty PNC Park.

Question: How did Nathan and Karen travel to visit Paul?
Answer: The took  an Amtrak train