Adding waves (of the same frequency) together

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  So, the general rule is,

  
  
     When two waves meet .... just ADD their wave functions together 
  
  

  The problem is that, in general, adding together two functions which look like this:

  

  is not really easy. In fact, it's a pain in the neck.

   
  
  
      Q:  Two travelling waves meet:
  
            y1  =  (5 cm) * sin ( 3 rad/m * x  -  0.1 rad/s * t )
  
            y2  =  (5 cm) * sin ( 3 rad/m * x  -  0.1 rad/s * t  +  1 rad )
  
  
          Is the amplitude of the combined wave 
  
                a)  bigger than either original wave
  
                b)  smaller than either original wave
  
                c)  the same as either original wave
  
  
          What is the SPEED of this combined wave?