William works thrice as fast as Carol. If William can complete the given task in 36 minutes, how long will it take to complete the task when both William and Carol works together?


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Answer:

27 minutes

Step by Step Explanation:
  1. Let William take 'y' minutes to complete the task.
  2. William is 3 times faster than that of Carol. It takes William to complete work in 36 minutes.
  3. So it takes Carol 3 × 36 = 108 minutes to complete the task.
  4. We know that for William, it takes 36 minutes to complete a task. So in 1 minute it will complete  
    1
    36
      of the task.
    So in 'x' minutes it will complete  
    x
    36
      of the task.
  5. We know that for Carol, it takes 108 minutes to complete a task. So in 1 minute it will complete  
    1
    108
      of the task.
    So in 'x' minutes it will fill  
    x
    108
      of the task.
  6. Since both William and Carol together complete the task so
     
    x
    36
      +  
    x
    108
      = 1 ...[1 referring to one complete task]
    or,  
    3x + x
    108
      = 1
    or, 4x = 108
    or, x =  
    108
    4
     
    or, x = 27
  7. When William and Carol works together, they will complete the work in 27 minutes.

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