Fast and hard are both adjectives and adverbs:
fast      ->        fast                  hard     ->        hard
Maria is a fast learner. (fast = adjective)
            Maria learns fast. (fast = adverb)
            James is a hard worker.  (hard = adjective)
            James works hard.  (hard = adverb)
 
We form the comparative of regular adverbs with more or less:
carefully          ->        more/less carefully
You should do your work more carefully.
She dose her work less carefully than other people.
 
The comparative of well is better:
            She speaks Arabic better than me.
 
The comparative of fast and hard are faster and harder:
            Could you walk faster? We are in hurry.
            You will have to work harder in future.