I want to ask:
For how long are you travelling to the Sea?
Welcher Satz ist richtig?
Wie lange fahren Sie ans Meer?
Für wie lange fahren Sie ans Meer?
I think you need to add für.
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"Wie lange fahren Sie ans Meer?" could be interpreted as "how long is the drive to the sea?" as well as "how long will you stay at the sea?". Which one of the two depends on the context.
"Für wie lange fahren Sie ans Meer?" on the other hand is a perfectly correct and legitimate question, which leaves no doubt about what is being asked (i.e. that you want to know how long your stay will be).
Oh, another way just came to my mind: "Wie lange fahren Sie bis ans/zum Meer?" would also be a precise question when asking for the during of the drive to reach the destination (i.e. the sea). (You could use either "ans" or "zum" - won't change the meaning at all.)
Both German sentences are correct, but they have different meanings.
Wie lange fahren Sie ans Meer? How long are you driving to the sea? – Here, fahren means the actual travel, and we want to know how long it will take to drive there.
Für wie lange fahren Sie ans Meer? For how long are you going to the sea? – In this case, fahren means "going away" or rather "being away", so we are wondering how long the person will be gone for.