GCSE Maths Practice: inverse-proportion

Question 8 of 10

This question checks whether you can recognise inverse proportion by testing if workers × time stays constant.

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\( \begin{array}{l}\text{Which examples show inverse proportion between workers and time?}\end{array} \)

Select all correct options:

How to Spot Inverse Proportion in GCSE Maths

This question is about recognising inverse proportion between the number of workers and the time taken to complete a job. In GCSE Maths, you often need to decide whether a situation shows direct proportion, inverse proportion, or neither. Being able to spot inverse proportion quickly is a valuable skill, especially in multiple-choice and multiple-answer questions.

The Key Idea

Inverse proportion means that as one quantity increases, the other decreases, while the overall task stays the same. For work problems, the task is the same “job”, so the total amount of work stays constant.

The rule is:

workers × time = constant

Method to Check Each Option

  1. Multiply the number of workers by the time for the first statement.
  2. Multiply the number of workers by the time for the second statement.
  3. If the products are equal, that pair is consistent with inverse proportion (same job, same rate per worker).

This works because if the job is the same, doubling workers should halve time, tripling workers should divide time by 3, and so on.

Worked Example (Not From the Options)

Example: 2 workers take 18 hours. 6 workers take 6 hours.

  • 2 × 18 = 36
  • 6 × 6 = 36
  • Products match, so this is inverse proportion.

Another Worked Example

Example: 4 machines take 9 hours. 12 machines take 3 hours.

  • 4 × 9 = 36
  • 12 × 3 = 36
  • Products match, so it shows inverse proportion.

Common Mistakes

  • Only looking at whether one goes up and the other goes down without checking the product.
  • Mixing up the rule and checking workers + time instead of workers × time.
  • Forgetting the “same job” assumption: inverse proportion only applies if the task and worker rate stay the same.
  • Arithmetic slips when multiplying, especially with larger numbers.

Real-Life Context

This idea appears in everyday teamwork. If more people help set up chairs for an event, it usually takes less time. In factories, more identical machines can reduce production time for a fixed number of items. These are real examples of inverse proportion (assuming everyone works at the same rate and there are no delays).

FAQs

Does workers × time always stay constant?
Only when workers are equally efficient and the job does not change.

What if the numbers don’t match exactly?
Then the pair is not showing perfect inverse proportion, or extra factors are affecting the time.

Study Tip

In multiple-choice questions, write a quick mini-table and calculate the products. It’s often faster and more reliable than trying to reason it out in your head.

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