GCSE Maths Practice: inverse-proportion

Question 7 of 10

This question tests inverse proportion using speed and time.

‹ ›

\( \begin{array}{l}\text{A train takes 2 hours at 80 km/h.} \\ \text{How long would the same journey take at 40 km/h?}\end{array} \)

Choose one option:

Inverse Proportion with Speed and Time

This question focuses on inverse proportion using speed and time, which is a key GCSE Maths concept. In inverse proportion, when one quantity decreases, the other increases so that something important stays the same. In speed problems, the quantity that stays the same is the distance travelled.

If a journey covers a fixed distance, travelling more slowly means it will take longer to arrive. This is why speed and time are inversely proportional.

The Key Rule

For all speed questions involving the same journey, remember:

speed × time = distance

If the distance stays constant, increasing or decreasing the speed must cause the time to change in the opposite way.

Step-by-Step Method

  1. Use the original speed and time to calculate the total distance.
  2. Keep this distance the same for the new speed.
  3. Divide the distance by the new speed to find the new time.

This structured approach helps avoid common GCSE mistakes.

Worked Example (Different Numbers)

Example: A bus travels for 3 hours at 70 km/h. How long would the same journey take at 35 km/h?

  • Distance = 70 × 3 = 210 km
  • New time = 210 ÷ 35
  • New time = 6 hours

Halving the speed doubles the travel time.

Another Example Using Slower Speed

Example: A car completes a journey in 1.5 hours at 100 km/h. How long would it take at 50 km/h?

  • Distance = 100 × 1.5 = 150 km
  • New time = 150 ÷ 50
  • New time = 3 hours

Reducing the speed increases the time required.

Common Mistakes to Avoid

  • Thinking speed and time are directly proportional.
  • Forgetting to calculate the distance first.
  • Multiplying when division is required.
  • Mixing up units such as minutes and hours.

Real-Life Applications

Inverse proportion between speed and time appears in everyday travel. Driving in heavy traffic increases journey time, while travelling faster on clear roads reduces it. Understanding this helps with realistic journey planning.

Frequently Asked Questions

Do I always need to find the distance?
Yes, unless the distance is already given. It must stay the same.

Is speed always inversely proportional to time?
Only when the distance does not change.

Study Tip

Before calculating, think logically: if the speed is lower, the journey must take longer. This quick check helps catch errors early.

Related Quizzes