Crossword Genius

Speed with which a rodent takes the last of the cheese (4)

Ross

I believe the answer is:

rate

'speed' is the definition.
(the speed at which something happens)

'a rodent takes the last of the cheese' is the wordplay.
'a rodent' becomes 'rat' (rat is a kind of rodent).
'takes' means one lot of letters go next to another.
'the last of' suggests the final letters.
The last letter of 'cheese' is 'e'.
'rat'+'e'='RATE'

'with which' acts as a link.

(Other definitions for rate that I've seen before include "Velocity" , "Bawl out" , "Tariff" , "Assign a value to something" , "Judge" .)

I've seen this clue in the Evening Standard.
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