First find half the number of guests at Carly's party: 30 guests / 2 = <<30/2=15>>15 guests
Then multiply that number by 2 for the number of burgers half the guests want: 15 guests * 2 burgers/guest = <<15*2=30>>30 burgers
Then add the 15 burgers for the 15 guests who only want 1 to find the total number of burgers: 30 burgers + 15 burgers = 45 burgers
Then divide the total number of burgers by the number of burgers Carly can cook at once to find the number of batches she cooks: 45 burgers / 5 burgers/batch = <<45/5=9>>9 batches
Then multiply the number of sides per burger by the cooking time per side to find each burger's total cook time: 4 minutes/side * 2 sides = <<4*2=8>>8 minutes
Finally, multiply each batch's cook time by the number of batches to find the total cook time: 8 minutes/batch * 9 batches = <<8*9=72>>72 minutes
#### 72