GCSE Maths Practice: direct-proportion

Direct Proportion Between Distance and Time

At Higher GCSE level, distance–time questions often involve fractional or decimal time values. These problems test whether you can combine proportional reasoning with accurate arithmetic. The key idea remains the same: when speed is constant, distance and time are directly proportional.

This means that if the time spent travelling increases by a certain factor, the distance travelled increases by the same factor. Understanding this relationship allows you to calculate distances for any given time once the speed is known.

Using Speed to Solve Proportion Problems

The link between distance, speed, and time is given by the formula:

distance = speed × time

Before this formula can be used, the speed must be found. Speed represents the distance travelled in one hour and acts as the unit rate in these problems.

Example: A cyclist travels 45 km in 1.5 hours. Dividing 45 by 1.5 gives a speed of 30 km/h. If the cyclist rides for 4 hours at the same speed, the distance travelled can be calculated by multiplying 30 by 4.

Why Fractional Time Values Matter

Higher-tier questions often use times such as 1.5 hours, 2.25 hours, or 0.75 hours. These values test your ability to divide and multiply accurately with decimals and fractions. Writing out each step clearly helps prevent errors.

Example: If a train travels 150 km in 2.5 hours, the speed is 60 km/h. Travelling for 3.75 hours at this speed would involve multiplying 60 by 3.75.

Common Mistakes to Avoid

• Forgetting to find the speed before calculating distance.
• Multiplying distance by time instead of dividing first.
• Misinterpreting decimal time values.
• Assuming answers must be whole numbers.

A useful sense check is to estimate roughly before calculating. If the time increases from about 1.5 hours to about 2.5 hours, the distance should increase by less than double.

Real-Life Applications

Distance–time proportional reasoning is used frequently in everyday life. Drivers plan journeys, delivery services estimate arrival times, and athletes analyse training performance. For example, if a runner maintains a steady pace of 12 km/h, they will cover 18 km in 1.5 hours and 30 km in 2.5 hours.

Frequently Asked Questions

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

Is it better to work in fractions or decimals?
Either is acceptable, but choose the form that you find clearer and less error-prone.

Study Tip

For Higher GCSE Maths questions, always write down the speed clearly before finding the distance. This helps organise your working and reduces mistakes under exam pressure.