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KCC's Quizzes AQQ230 about a clock and angle puzzle



		

			

									
					    KCC
					
							

			
				
									
											
			
			
				
  •  Analog Employees  

			
			
			    	
			                    
                
				                on Mar 13, 2023 
				
			
			
		


				
		

		    		    
		    
		    	
			
 


In an analog clock, the angle formed by the hour and the minute hands varies constantly.


Questions:


    

  1. Which angle θ is obtained when it is 5:20 ?
    2. 

  2. Determine when exactly at around 4, the angle will be exactly 90°?
    3. 


										


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[edited by: emassa at 1:54 PM (GMT -4) on 29 Mar 2023]
				

					


				
				
		

			
						
									
									
						
						
			
			
			
			
		


        
        
    
        
    
            
                

            

               

                    
                        
                        
                    
               
 
               
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    •  Analog Employees  
    
            
			                            
                        
                on Mar 14, 2023 4:33 AM
            
            
					
    
	
    

		
		
    
					
    1. θ = 40°
    

    Solution:
    

    θ from 12 for each number = 360° / 12 = 30°
    

    Hour θ movement for each minute = 30° / 60 = 0.5°
    

    For 20 minutes,
    

    number = 4
    

    θ = 4 (30°) = 120°
    

    For 5,
    

    θ = 5 (30°) = 150°
    

    Hour θ movement = 20 (0.5°) = 10°
    

    Total = 150° + 10° = 160°
    

    θ difference = 160° - 120° = 40°
    

    2. 4:05 (minute is 5.45 to be exact)
    

    Solution:
    

    θ from 12 for each number = 360° / 12 = 30°
    

    Hour θ movement for each minute = 30° / 60 = 0.5°
    

    θ for each minute = 360° / 60 = 6°
    

    For 4,
    

    θ = 4 (30°) = 120°
    

    Equation for 90°:
    

    90° = [120° + x (0.5°)] - x (6°)
    

    90° = [120° + 0.5°x] - 6°x
    

    6°x - 0.5°x = 120° - 90°
    

    5.5°x = 30°
    

    x = 5.45
    

    Time would be 4:05 (5.45 to be exact)
    
			
    

		
		
		
		
	
    
	
    
		
    
			
		
    
	
    
	
    
		
						
				
				
						
				
				
		
		
    
			
		
    
	
    

    

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    •  Analog Employees  
    
            
			                            
                        
                on Mar 14, 2023 4:33 AM
            
            
					
    
	
    

		
		
    
					
    1. θ = 40°
    

    Solution:
    

    θ from 12 for each number = 360° / 12 = 30°
    

    Hour θ movement for each minute = 30° / 60 = 0.5°
    

    For 20 minutes,
    

    number = 4
    

    θ = 4 (30°) = 120°
    

    For 5,
    

    θ = 5 (30°) = 150°
    

    Hour θ movement = 20 (0.5°) = 10°
    

    Total = 150° + 10° = 160°
    

    θ difference = 160° - 120° = 40°
    

    2. 4:05 (minute is 5.45 to be exact)
    

    Solution:
    

    θ from 12 for each number = 360° / 12 = 30°
    

    Hour θ movement for each minute = 30° / 60 = 0.5°
    

    θ for each minute = 360° / 60 = 6°
    

    For 4,
    

    θ = 4 (30°) = 120°
    

    Equation for 90°:
    

    90° = [120° + x (0.5°)] - x (6°)
    

    90° = [120° + 0.5°x] - 6°x
    

    6°x - 0.5°x = 120° - 90°
    

    5.5°x = 30°
    

    x = 5.45
    

    Time would be 4:05 (5.45 to be exact)
    
			
    

		
		
		
		
	
    
	
    
		
    
			
		
    
	
    
	
    
		
						
				
				
						
				
				
		
		
    
			
		
    
	
    

    

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