GCSE Maths Practice: inverse-proportion

Question 5 of 10

This question tests inverse proportion using workers and time for a fixed task.

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\( \begin{array}{l} \text{It takes 6 workers 15 hours to complete a task.} \\ \text{How long would it take 10 workers to complete the same task?} \end{array} \)

Choose one option:

Inverse Proportion with Workers and Time (Higher Tier)

This question tests your understanding of inverse proportion using workers and time, a common Higher GCSE Maths topic. In these problems, the task itself does not change — only the number of workers and the time taken change.

The Constant Quantity

For work-based inverse proportion questions, the key idea is that the total amount of work remains the same. This is often measured in worker-hours:

number of workers × time = total work

If more workers are available to do the same task, the work can be shared, so the time needed decreases.

Why This Is Inverse Proportion

Inverse proportion occurs when one quantity increases while the other decreases, and the overall outcome stays fixed. In this case, increasing the number of workers reduces the number of hours required to complete the task.

Step-by-Step Strategy

  1. Identify the two variables (workers and time).
  2. Calculate the total amount of work using the given values.
  3. Keep this total constant.
  4. Set up an equation with the new number of workers.
  5. Solve to find the missing time.

This structured approach is especially important for Higher-tier questions, where numbers may not be simple multiples.

Worked Example (Different Numbers)

Example: 8 workers complete a task in 12 hours. How long would it take 16 workers?

  • Total work = 8 × 12 = 96 worker-hours
  • 16 × t = 96
  • t = 6 hours

Doubling the number of workers halves the time.

Another Worked Example

Example: 12 workers take 5 hours to complete a job. How long would it take 4 workers?

  • Total work = 12 × 5 = 60 worker-hours
  • 4 × t = 60
  • t = 15 hours

Fewer workers means more time is required.

Common Higher-Tier Mistakes

  • Using direct proportion instead of inverse proportion.
  • Forgetting to calculate total work first.
  • Mixing up multiplication and division.
  • Not checking whether the final answer is reasonable.

Real-World Context

Inverse proportion with workers is used in construction, project management, and event planning. Managers often estimate how changing team size affects completion time, assuming everyone works at the same rate.

Exam Tip

When a question says “the same task” or “the same job”, immediately write workers × time = constant before doing any calculations.

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