What is the difference between "like" and "as"?

[Rita]

Test No. incompl/inter-53 "Business Expressions (2)", question 3

She was very enthusiastic about her new job and was making rapid progress ......... nobody's business.

(a) as
(b) with
(c) similar
(d) like

Test No. incompl/inter-53 "Business Expressions (2)", answer 3

She was very enthusiastic about her new job and was making rapid progress like nobody's business.

Correct answer: (d) like
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Could you tell me please why word "as" doesn't fit ?
Regards
Rita

[Alan]

The comparison is with the noun not the verb.
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English as a Second Language
You can read my ESL story Phrasal Verbs/take