GCSE Maths Practice: direct-proportion

Question 4 of 10

This question tests your understanding of direct proportion using distance and time.

‹ ›

\( \begin{array}{l}\text{A car travels 90 km in 2 hours.} \\ \text{How far will it travel in 5 hours at the same speed?}\end{array} \)

Choose one option:

Find the distance travelled in one hour before scaling up to the total time.

Direct Proportion in Distance and Time

Direct proportion is commonly used to describe the relationship between distance and time when speed remains constant. In GCSE Maths, these questions often involve finding how far an object travels when the time changes but the speed stays the same. This type of problem is very practical and reflects real-life situations such as driving, cycling, and walking.

When distance and time are directly proportional, increasing the time spent travelling will increase the distance covered at the same rate. If the time doubles, the distance doubles. If the time triples, the distance triples. This only works when the speed does not change.

Using Speed to Solve Direct Proportion Problems

The key idea behind distance–time questions is speed. Speed tells us how much distance is travelled in one unit of time. Once the speed is known, it can be multiplied by any amount of time to find the total distance.

Example: A cyclist travels 60 km in 3 hours. To find the speed, divide 60 by 3, giving 20 km per hour. If the cyclist rides for 4 hours at the same speed, the distance travelled will be 20 × 4 = 80 km.

Why Unit Rates Matter

Finding the distance travelled in one hour is called finding the unit rate. This step makes it much easier to solve direct proportion problems because it creates a simple and repeatable method. Once the unit rate is known, you can calculate the distance for any length of time.

Example: If a train travels 150 km in 5 hours, the distance per hour is 30 km. Travelling for 2 hours at this speed would cover 60 km.

Common Mistakes to Avoid

  • Forgetting to divide to find the distance per hour.
  • Multiplying the original distance by the new time directly.
  • Mixing up hours and minutes without converting units.
  • Assuming speed changes when the question says it stays the same.

Always check whether your answer is reasonable. If the journey takes longer, the distance travelled should increase.

Real-Life Applications

This type of calculation is used frequently in real life. Drivers estimate how far they can travel before refuelling, delivery companies calculate journey times, and athletes track performance during training. For example, if a runner maintains a steady pace of 10 km per hour, they can expect to cover 15 km in 1.5 hours.

Frequently Asked Questions

Do distance and time always follow direct proportion?
No. Direct proportion only applies when speed is constant. If speed changes, the relationship is no longer directly proportional.

Why should I find the distance per hour first?
It reduces confusion and works for any time value, making it ideal for exam questions.

Study Tip

In GCSE Maths exams, always write down the speed or distance per hour first. This helps structure your working and improves accuracy under time pressure.

Related Quizzes