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Rate Problems - How Long Will it Take if Janet and Michael Work Together

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Does the Answer Make Sense?

Gene, Michael, and Janet are choreographing a music video.  Alone, Gene takes 8 hours to do the job, Michael takes 3 hours to do the job, and Janet takes 1 hour to do the job.

What is the ratio of Gene working alone to Michael and Janet working together? 32:3

Verify the Answer

Time:

  1. 1 = Michael's rate * t + Janet's rate * t
  2. 1= (1/3) * t + (1) * t
  3. 1= (1/3) * (3/4) + (1) * (3/4)
  4. 1 = (3/12) + (3/4)
  5. 1 = (1/4) + (3/4)
  6. 1 = 1

Ratio:

8:(3/4) = 8/(3/4) = 8 ÷ (3/4) = 32/3


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