Solved the problem of keeping fit (6,3)
I believe the answer is:
worked out
'keeping fit' is the definition.
The answer and definition are different parts of speech. However, past participle verbs and adjectives sometimes mean the same thing.
'solved the problem' is the wordplay.
'solved' becomes 'worked' ('work' can be a synonym of 'solve').
'the problem' becomes 'out' (I am not sure about this - if you are sure you should believe this answer much more).
'worked'+'out'='WORKED OUT'
'of' is the link.
Can you help me to learn more?
(Other definitions for worked out that I've seen before include "Went training" , "planned" .)