GCSE Maths Practice: inverse-proportion

Question 5 of 10

This question tests inverse proportion using speed and time.

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\( \begin{array}{l}\text{A journey takes 3 hours at 60 km/h.} \\ \text{How long would the same journey take at 90 km/h?}\end{array} \)

Choose one option:

Inverse Proportion with Speed and Time

This question involves inverse proportion using speed and time, a very common GCSE Maths topic. In inverse proportion, when one quantity increases, the other decreases so that something else stays the same. In this case, the thing that stays the same is the distance travelled.

When travelling a fixed distance, increasing the speed means the journey takes less time. Slowing down means the journey takes longer. This is why speed and time are inversely proportional.

The Key Relationship

For speed problems involving the same journey, the rule is:

speed × time = distance

If the distance does not change, the product of speed and time must stay constant.

Step-by-Step Method

  1. Use the original speed and time to calculate the 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 method works for all GCSE speed questions where the distance stays the same.

Worked Example (Different Numbers)

Example: A car travels for 4 hours at 50 km/h. How long would the same journey take at 100 km/h?

  • Distance = 50 × 4 = 200 km
  • New time = 200 ÷ 100
  • New time = 2 hours

Doubling the speed halves the time.

Another Example Using Slower Speed

Example: A train takes 2 hours to travel a route at 90 km/h. How long would it take at 60 km/h?

  • Distance = 90 × 2 = 180 km
  • New time = 180 ÷ 60
  • New time = 3 hours

Reducing the speed increases the travel time.

Common Mistakes to Avoid

  • Assuming speed and time are directly proportional.
  • Forgetting to calculate the distance first.
  • Multiplying when you should divide.
  • Mixing up units, such as minutes and hours.

Real-Life Applications

This type of inverse proportion appears in everyday life. For example, driving faster on a motorway reduces travel time, while traffic congestion increases it. Understanding this relationship helps with journey planning and estimating arrival times.

Frequently Asked Questions

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

Is this always inverse proportion?
Yes, if the distance is fixed and only speed and time change.

Study Tip

Before calculating, ask yourself whether the time should be longer or shorter. This quick check helps you spot mistakes before finishing the question.

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