Crossword Genius

American Indian leaving hospital very quickly (5)

Ross

I believe the answer is:

apace

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'very quickly' is the definition.

'american indian leaving hospital' is the wordplay.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'indian leaving hospital' becomes 'pace' (I can't justify this - if you can you should believe this answer much more).
'a'+'pace'='APACE'

Can you help me to learn more?

(Other definitions for apace that I've seen before include "fast" , "at high speed" , "At a rapid rate" , "Swiftly, quickly" , "What's quickly" .)

I've seen this clue in The Times.
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