Fleet Street contains a mixture of printers (5)

I believe the answer is:

rapid

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'fleet' is the definition.
(I've seen this before)

'street contains a mixture of printers' is the wordplay.
'street' becomes 'rd'.
'contains' is an insertion indicator.
'mixture of printers' becomes 'pi' (I can't justify this - if you can you should believe this answer much more).
'a'+'pi'='api'
'rd' enclosing 'api' is 'RAPID'.

Can you help me to learn more?

(Other definitions for rapid that I've seen before include "Fleet, swift" , "Happening quickly" , "Expeditious" , "Swift, speedy" , "Prompt" .)

I've seen this clue in The Globe and Mail.

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