Late for work vs Late at work

[Cho Yung]

English Grammar Tests, Elementary Level

ESL/EFL Test #91 "Using Prepositions", question 1

Ralph was late ......... work again. He may be fired.

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

English Grammar Tests, Elementary Level

ESL/EFL Test #91 "Using Prepositions", answer 1

Ralph was late for work again. He may be fired.

Correct answer: (c) for

Your answer was: incorrect
Ralph was late at work again. He may be fired.
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why is it the preposition "for" is incorrect in this sentence?

Cho Yung

[Alan]

Hi,

'Late for work' suggests late in attending/coming to work.

Alan
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English as a Second Language
You can read my ESL story A day in the life of a policeman

[Joydaniel2000]

please explain why it is NOT late at work