This is the 316th most frequent Czech word.
rychle
Quickly.
The word 'rychle' functions here as an adverb modifying the verb 'běžím' (to run) and describes the manner of the action (running quickly).
Běžím rychle, abych stihl vlak.
I am running quickly to catch the train.
Here, 'rychlý' is an adjective describing 'vůz' (car) and indicates its characteristic (being fast).
Ten vůz je rychlý a moderní.
That car is fast and modern.
In this sentence, 'rychle' is used as an adverb indicating the manner in which the action (solving a problem) should be performed (quickly).