Took nutrition at end of race (3)

I believe the answer is:

ate

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'took nutrition' is the definition.
'ate' can be an answer for 'took' (eating is a kind of taking). I'm unsure of the 'nutrition' bit.

'at end of race' is the wordplay.
'end of' says to take the final letters.
The last letter of 'race' is 'e'.
'at'+'e'='ATE'

Can you help me to learn more?

(Other definitions for ate that I've seen before include "Took food" , "Consumed food" , "Munched" , "Tea (anag.)" , "Had at meal" .)

I've seen this clue in The Times.

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