"out at sea" vs "out for sea"

[Rosa Rimli]

English Language Proficiency Tests, Advanced Level

ESL/EFL Test #664 "Prepositional Phrases - At, By, For and To (2)", question 5

My brother is in the Navy and he is coming home on leave in a week. He has been out ......... sea for more than six months now and I miss him.

(a) at
(b) by
(c) for
(d) to

English Language Proficiency Tests, Advanced Level

ESL/EFL Test #664 "Prepositional Phrases - At, By, For and To (2)", answer 5

My brother is in the Navy and he is coming home on leave in a week. He has been out at sea for more than six months now and I miss him.

Correct answer: (a) at

Your answer was: incorrect
My brother is in the Navy and he is coming home on leave in a week. He has been out for sea for more than six months now and I miss him.
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How at sea is correct,why not for sea? What is the difference?

Rosa Rimli

[Mister Micawber]

'For' is not used in this collocation.
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Native English teacher at Mister Micawber's