peg away
phrasal verb
            
              pegged away; pegging away; pegs away            
        
    
        chiefly British,  informal      
      
                                
                                
              
          
                                                      : to work hard                                      
                
                  —usually + at
He sat there pegging away at his homework.
    
                
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  Merriam-Webster unabridged




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