GCSE Maths Practice: inverse-proportion

Question 2 of 10

This question tests inverse proportion using speed and time for a fixed distance.

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\( \begin{array}{l} \text{A cyclist takes 3 hours to cover a distance at 16 km/h.} \\ \text{How long would it take to cover the same distance at 24 km/h?} \end{array} \)

Choose one option:

Inverse Proportion with Speed and Time (Higher Tier)

This question tests your understanding of inverse proportion using speed and time, a key Higher GCSE Maths topic. When travelling the same distance, speed and time are inversely proportional: increasing the speed reduces the time taken, while decreasing the speed increases the time taken.

The Constant Quantity

In speed problems like this one, the quantity that stays constant is the distance travelled. This leads to the core relationship:

speed × time = distance

If the distance does not change, the product of speed and time must remain the same.

Why This Is Inverse Proportion

If the cyclist travels faster, each hour covers more distance. As a result, fewer hours are needed to complete the same journey. This opposite movement of the two variables is what defines inverse proportion.

Step-by-Step Strategy

  1. Use the given speed and time to calculate the distance.
  2. Keep this distance fixed.
  3. Divide the distance by the new speed to find the new time.

This structured approach is especially important in Higher-tier questions, where decimals and unfamiliar speeds are common.

Worked Example (Different Numbers)

Example: A runner completes a route in 2.5 hours at 12 km/h. How long would the same route take at 20 km/h?

  • Distance = 12 × 2.5 = 30 km
  • New time = 30 ÷ 20
  • New time = 1.5 hours

Increasing the speed reduces the time taken.

Another Worked Example

Example: A car travels a fixed distance in 1.2 hours at 75 km/h. How long would it take at 60 km/h?

  • Distance = 75 × 1.2 = 90 km
  • New time = 90 ÷ 60
  • New time = 1.5 hours

Reducing the speed increases the travel time.

Common Higher-Tier Mistakes

  • Forgetting to calculate the distance first.
  • Assuming speed and time are directly proportional.
  • Mishandling decimals when multiplying or dividing.
  • Not checking whether the final answer makes sense.

Real-World Context

Inverse proportion between speed and time is used in journey planning, logistics, and sports performance. Understanding this relationship helps estimate arrival times and compare travel options accurately.

Exam Tip

When a question mentions the same distance or same route, immediately write down speed × time = constant. This helps you avoid choosing a direct proportion method by mistake.

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