You did say "fastest", right? Of course, by air. Vietnam Airlines offers 4 flights daily and it takes just over an hour and it costs around $ 76/person/one way. http://www.tnktravelvietnam.com/html/ticket_airlin...
As for the train, there are also several each day but it takes 14 hours at least to get from Hanoi to Hue. It's pretty cheap though as you pay only about $ 21 for a good ticket one way.
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You did say "fastest", right? Of course, by air. Vietnam Airlines offers 4 flights daily and it takes just over an hour and it costs around $ 76/person/one way. http://www.tnktravelvietnam.com/html/ticket_airlin...
As for the train, there are also several each day but it takes 14 hours at least to get from Hanoi to Hue. It's pretty cheap though as you pay only about $ 21 for a good ticket one way.
Vietnam Airline.
Take the Train, it is a way more memorable experience and cheaper.