Not a teacher.
We use these two structures to say how long to do sth:
-It + take + period of time + (for sb) + to do sth
-S + spend +period of time + doing sth
So I think 'to fix' is the best answer for the question. 'ages' here means great length of time (Ages Definition | Definition of Ages at Dictionary.com)
St takes time (for sb) to do st.
If you want to use "Verb-ing", you can use the word "spend" for instead.
For instance, "I will spend ages fixing them"