GCSE Maths Practice: inverse-proportion

Question 6 of 10

This question tests inverse proportion using pipes and time.

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\( \begin{array}{l}\text{Two pipes fill a tank in 12 minutes.} \\ \text{How long would it take four pipes to fill the same tank?}\end{array} \)

Choose one option:

Inverse Proportion with Pipes and Time

This question is based on inverse proportion, a GCSE Maths topic that often appears in problems involving pipes, taps, workers, or machines. In inverse proportion, when one quantity increases, the other decreases so that the overall result remains unchanged.

In pipe problems, the important idea is that the total volume of water being moved stays the same. Whether fewer pipes take longer or more pipes take less time, the tank being filled does not change.

The Key Relationship

For questions involving pipes and time, the rule is:

number of pipes × time taken = constant

This shows that doubling the number of pipes halves the time needed.

Step-by-Step Method

  1. Identify the two linked quantities (pipes and time).
  2. Multiply the given values to find the total work or volume.
  3. Keep this total the same for the new number of pipes.
  4. Solve the equation to find the missing time.

This method works for all GCSE pipe questions where each pipe works at the same rate.

Worked Example (Different Numbers)

Example: 3 pipes fill a tank in 10 minutes. How long would it take 6 pipes?

  • Total work = 3 × 10 = 30
  • 6 × t = 30
  • t = 5 minutes

Doubling the number of pipes halves the filling time.

Another Example Using More Pipes

Example: 4 taps can fill a container in 15 minutes. How long would it take 12 taps?

  • Total work = 4 × 15 = 60
  • 12 × t = 60
  • t = 5 minutes

Tripling the number of taps reduces the time to one third.

Common Mistakes to Avoid

  • Assuming more pipes means more time.
  • Using direct proportion instead of inverse proportion.
  • Adding values instead of multiplying.
  • Forgetting that the volume of water stays the same.

Real-Life Applications

Inverse proportion with pipes appears in plumbing, irrigation, and drainage systems. Adding more pipes or outlets usually speeds up filling or emptying, while fewer pipes slow the process down.

Frequently Asked Questions

Does this work if pipes have different flow rates?
No. This method assumes all pipes work at the same rate.

Is this always inverse proportion?
Yes, as long as the tank size stays the same.

Study Tip

Before calculating, ask yourself whether the time should increase or decrease. If more pipes are used, the time must be shorter.

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