Machines A and B always operate independently and at their respective constant rates. When working alone, Machine A can fill a production lot in 3 hours, and Machine B can fill the same lot in x hours. If A and B worked alternatively, while each work for 1 hour at a time, the total work gets completed in 4 hours. What is the value of x? A)8 B)9 C)6 D)5 E)7

• A = 1/3; B = 1/x
  Both fill it 4 hours alternatively, i.e. each fills in 2 hours
  Thus, A = 2 x 1/3 = 2/3
  B = 2 x 1/x = 2/x
  and, 2/3 + 2/x = 1
  Thus, x = 6
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