A speed I took to be the correct rate to get there (12)
I believe the answer is:
amphitheatre
'be the correct rate to get there' is the definition.
I can't tell whether this defines the answer.
'a speed i took' is the wordplay.
'speed' becomes 'mph' (miles per hour).
'took' becomes 'theatre' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'a'+'mph'+'i'+'theatre'='AMPHITHEATRE'
'to' is the link.
Can you help me to learn more?
(Other definitions for amphitheatre that I've seen before include "Roman tiered arena" , "Large oval stadium with tiers of seats" , "Open auditorium" , "Classical home for drama" , "Classical performance area" .)