GCSE Maths Practice: direct-proportion

Question 9 of 10

This question tests your ability to recognise direct proportion between distance and time.

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\( \begin{array}{l}\text{Which of the following show direct proportion between distance and time (at constant speed)?}\end{array} \)

Select all correct options:

Check whether distance scales by the same factor as time.

Recognising Direct Proportion Between Distance and Time

Direct proportion is commonly used to describe the relationship between distance and time when speed remains constant. In GCSE Maths, questions like this test whether students can recognise consistent patterns rather than simply perform calculations. Understanding the concept behind the numbers is just as important as being able to calculate an answer.

When distance and time are directly proportional, the distance travelled increases steadily as time increases. This means that the speed stays the same throughout the journey. If the time taken doubles, the distance travelled should also double. If the time is halved, the distance should halve as well.

Using Constant Speed to Check Proportion

The key idea in distance–time proportion questions is constant speed. Speed is calculated using the formula:

speed = distance ÷ time

If the speed is the same in each situation being compared, then the relationship shows direct proportion.

Example: A car travels 80 km in 2 hours. The speed is 40 km per hour. If the same car travels for 5 hours at the same speed, it will cover 200 km. The distance increases at the same rate as time, confirming direct proportion.

Doubling and Halving as a Quick Check

In Foundation-level questions, numbers are often chosen so that doubling or halving is easy to spot. This allows you to check direct proportion quickly without detailed calculations.

Example: If travelling for 3 hours results in a distance of 75 km, then travelling for 6 hours at the same speed should result in 150 km. If the distance does not double when the time doubles, the relationship is not directly proportional.

Common Mistakes to Avoid

  • Assuming any increase in distance means direct proportion.
  • Forgetting that speed must stay constant.
  • Comparing distances without considering the time taken.
  • Mixing up direct proportion with inverse proportion.

A helpful sense check is to ask: if the journey takes longer at the same speed, should the distance increase by the same factor?

Real-Life Applications

This concept is widely used in everyday life. Drivers estimate how far they can travel in a given time, delivery companies plan routes, and athletes track training distances. For example, if a runner maintains a steady pace of 12 km per hour, they will cover 18 km in 1.5 hours and 36 km in 3 hours.

Frequently Asked Questions

Does distance always increase in direct proportion to time?
No. Direct proportion only applies when speed is constant. If speed changes, the relationship is no longer directly proportional.

Do I need to calculate speed every time?
Not always. In many questions, spotting simple scaling such as doubling or halving is enough.

Study Tip

In GCSE Maths multiple-answer questions, check every option carefully. More than one example may show direct proportion, so avoid choosing just one unless the question tells you to.

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