Kenneth ChengMathematical modeling
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Two workers take 4 and 3 hours separately for one job. At constant additive rates, how long do they take together for five identical jobs?

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TOPIC 01

2021 JM01

Averaging 4 and 3 would not give a joint work rate.

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01 / Standard#Your turn

Two workers take 4 and 3 hours separately for one job. At constant additive rates, how long do they take together for five identical jobs?

Official paper · jm01-2021 · I.2 · PDF 2

Official original and suggested answers ↗ · Suggested answer PDF page 5

Skills and prerequisite lessons
  1. Option A32/532/5
  2. Option B35/435/4
  3. Option C35/235/2
  4. Option D20/320/3
  5. Option E60/760/7

Working and explanation

BUILD THE REASONING

Hint 1
Add jobs-per-hour rates, not completion times.
Hint 2
Divide the total five jobs by the combined rate.
Worked solution

  1. Express the two individual rates.

    r=1/4+1/3=7/12r=1/4+1/3=7/12

  2. Use time=amount/rate.

    T=5/(7/12)=60/7T=5/(7/12)=60/7

E: 60/7 hours.

Checks and common pitfalls: Averaging 4 and 3 would not give a joint work rate.

Reasoning checklist · self / teacher assessment
  • Teaching assessment checklist, independently authored. Use the original paper for official marks.
  • Express the two individual rates.
    r=1/4+1/3=7/12r=1/4+1/3=7/12
  • Use time=amount/rate.
    T=5/(7/12)=60/7T=5/(7/12)=60/7

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Curriculum and source notes ↗