GCSE Maths Practice: inverse-proportion

Question 3 of 10

This question tests inverse proportion using printing speed and time.

‹ ›

\( \begin{array}{l} \text{A printer can finish 60 pages in 12 minutes.} \\ \text{How long would it take to finish 180 pages at triple speed?} \end{array} \)

Choose one option:

Inverse Proportion with Rates and Speed (Higher Tier)

This question tests your understanding of inverse proportion using printing speed and time. At Higher GCSE level, inverse proportion questions often involve rates rather than simple counts of workers or machines. Being confident with rates such as “pages per minute” is essential.

What Stays Constant?

In this problem, the constant quantity is the total number of pages printed. Whether the printer works slowly or quickly, the total output remains the same. This means:

printing speed × time = total pages

If the printing speed increases, the time required must decrease for the same number of pages. This opposite movement is what defines inverse proportion.

Why Speed Matters

Speed tells us how much work is done per unit of time. When speed is multiplied by a factor, the time taken is divided by the same factor, provided the total amount of work does not change.

Step-by-Step Strategy

  1. Calculate the original printing rate.
  2. Adjust the rate according to the speed change.
  3. Divide the total number of pages by the new rate.

This approach avoids confusion and keeps the working clear for examiners.

Worked Example (Different Numbers)

Example: A printer produces 80 pages in 16 minutes. How long would it take to print 200 pages if the speed doubles?

  • Original speed = 80 ÷ 16 = 5 pages per minute
  • Doubled speed = 10 pages per minute
  • Time = 200 ÷ 10 = 20 minutes

Doubling the speed halves the time needed per page.

Another Worked Example

Example: A copier prints 150 pages in 30 minutes. How long would it take to print 300 pages at the same speed?

  • Speed = 150 ÷ 30 = 5 pages per minute
  • Time = 300 ÷ 5 = 60 minutes

This example shows that if the speed does not change, time is directly proportional to the number of pages.

Common Higher-Tier Mistakes

  • Forgetting to calculate the rate first.
  • Assuming time is directly proportional to speed.
  • Multiplying instead of dividing when speed increases.
  • Ignoring the phrase “triple speed”.

Real-World Context

Understanding inverse proportion with rates is useful in offices, factories, and digital systems. Faster machines reduce waiting time, while slower speeds increase it. This logic also applies to data transfer rates and download times.

Exam Tip

Whenever you see phrases like “double speed”, “triple speed”, or “half speed”, immediately think inverse proportion and work with rates.

Related Quizzes