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KCC's quiz AQQ274 about 2 sportsmen running and walking



		

			

									
					    KCC
					
							

			
				
									
											
			
			
				
  •  Analog Employees  

			
			
			    	
			                    
                
				                on Nov 21, 2024 
				
			
			
		


				
		

		    		    
		    
		    	
			
Two  sportsmen A and B have exactly the same running speed and the same walking speed.


One day they started the same trip to the same place.


Sportsman-A walked for half of the distance and ran for the rest, while


Sportsman-B walked for half the time and ran for the other half of time.


Question: Which sportsman reached the end of the trip first? How do you justify it?


 


Good luck and try to be among the firsts!


P.S. Pass those quizzes among your colleagues and friends; we all need such small brainstorming time to time!

									
			        
		


				
						
        

    
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                on Nov 22, 2024 6:54 AM
            
            
					
      
	
      

		
		
      
					
      Let R equal running speed and W equal walking speed.
      

      Time for A to travel distance D:  D/2W+D/2R = (D/2)[1/W+1/R] = D(W+R)/2WR
      

      Time for B to travel distance D:  2D/(W+R)
      

      Let W=kR where 0< k <1:  Walking speed less than running speed
      

      Ta/Tb = [(W+R)^2]/4WR = [(k+1)^2]/4k
      

      If Ta/Tb < 1 then k^2+2k+1<4k or (k-1)^2<0 :FALSE
      

      If Ta/Tb > 1 then k^2+2k+1>4k or (k-1)^2>0 :TRUE
      

      Therefore, Tb is less then Ta and sportsman B finishes first.
      
			
      

		
			
	      

		
		
	
      
	
      
		
      
			
		
      
	
      
	
      
		
						
				
				
						
				
				
		
		
      
			
		
      
	
      

      

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                on Nov 22, 2024 6:54 AM
            
            
					
        
	
        

		
		
        
					
        Let R equal running speed and W equal walking speed.
        

        Time for A to travel distance D:  D/2W+D/2R = (D/2)[1/W+1/R] = D(W+R)/2WR
        

        Time for B to travel distance D:  2D/(W+R)
        

        Let W=kR where 0< k <1:  Walking speed less than running speed
        

        Ta/Tb = [(W+R)^2]/4WR = [(k+1)^2]/4k
        

        If Ta/Tb < 1 then k^2+2k+1<4k or (k-1)^2<0 :FALSE
        

        If Ta/Tb > 1 then k^2+2k+1>4k or (k-1)^2>0 :TRUE
        

        Therefore, Tb is less then Ta and sportsman B finishes first.
        
			
        

		
			
	      

		
		
	
        
	
        
		
        
			
		
        
	
        
	
        
		
						
				
				
						
				
				
		
		
        
			
		
        
	
        

        

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