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The AirTrain fare will be payable at the Jamaica AirTrain terminal. AirTrain fare is $5.00, and is payable with a Metrocard. Metrocard vending machines are available at the terminal. The subway fare is $2.25 if paid by Metrocard; $2.50 if paid by a single-ride ticket. For you, it sounds like you should buy a $7.25 Metrocard when you get off the AirTrain. You will swipe it at the AirTrain terminal, and $5.00 will be deducted from the card, leaving $2.25 for the subway.

There is no need to walk to the Sutphin Boulevard/Hillside Avenue F station; just catch the E train at the Sutphin Boulevard/Archer Station below the Jamaica AirTrain terminal. Take the E to Lexington Avenue/53rd Street station, where you can transfer to the uptown 6 train, or pick up an uptown Third Avenue bus at 53rd and Third. A subway-bus transfer is free if you use a Metrocard, and transfer within two hours of entering the subway.

If you prefer to take the F to 63rd Street and transfer to the Third Avenue bus, just take the E from Sutphin/Archer, and transfer to the F at Union Turnpike/Kew Gardens or Continental Avenue/Forest Hills.

FYI: With the exception of a few rush-hour trains, the E train no longer runs to or from 179th Street/Hillside, and therefore no longer serves Sutphin/Hillside. The E and F lines now diverge east of the Briarwood/Van Wyck station, and the F now makes all stops at all times between 179th Street and Continental Avenue/Forest Hills. The E now runs along the (relatively) new Archer Avenue line to stops at Jamaica/Van Wyck, Sutphin/Archer/JFK, and Parsons/Archer, a/k/a Jamaica Center.