JFK from midtown via subway

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Does anyone have experience with this?

I'm going to JFK tonight and plan to take the subway for there for the second time (first time from this area, and the first time was so impromptu and rushed and panicked anyway that I am lucky that I ended up in the right place).  I'll be leaving from the Grand Central subway stop.

Just to make sure I don't do this wrong...

I want to take the 6 up to 51st, switch to the Queens-bound E towards Jamaica, and then switch to the Airtrain at Sutphin Blvd, right?

How long would you allow from door (door being Grand Central) to terminal during rush hour (will leave at around 6)?

Thanks so much!