Speed, distance and time questions appear on virtually every GCSE Maths paper. They test your ability to rearrange a formula, convert units and interpret real-world contexts — all skills that examiners love to assess. Whether you are working out average speed on a Foundation paper or analysing a multi-stage journey on Higher, the same core relationship applies. This guide sets out the key formulas, walks through clear examples at both tiers, highlights the traps students fall into, and provides practice questions so you can build confidence before your exam. For a wider list of must-know formulas, visit our GCSE Maths formulas guide.
What Is the Speed, Distance and Time Relationship?
Speed tells you how far something travels in a given amount of time. The three quantities are linked by:
$$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$$
From this, you can rearrange to find any one of the three:
$$\text{Distance} = \text{Speed} \times \text{Time}$$
$$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$$
The Formula Triangle
Many students find it helpful to picture the DST triangle: Distance sits on top, with Speed and Time on the bottom. Cover the quantity you want to find, and the remaining two show you the formula.
Units
The most common units at GCSE are:
- Speed: miles per hour (mph), kilometres per hour (km/h), or metres per second (m/s).
- Distance: miles, kilometres, or metres.
- Time: hours, minutes, or seconds.
Critical rule: the units must be consistent. If speed is in km/h, distance must be in km and time in hours. If time is given in minutes, convert to hours first (divide by 60) — or convert speed to km/min.
Average Speed
Average speed is the total distance divided by the total time, not the mean of two speeds. This is a frequent source of error.
$$\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}$$
Step-by-Step Method
- Read the question carefully and identify which quantity you need to find (speed, distance, or time).
- Write down the formula you need.
- Check units. Convert minutes to hours, metres to kilometres, etc., as needed.
- Substitute values into the formula.
- Calculate and give your answer with correct units.
- For multi-stage journeys, find the distance and time for each stage separately, then use totals to find the overall average speed.
Converting Time
- Minutes to hours: divide by 60. For example, 45 minutes = 45 ÷ 60 = 0.75 hours.
- Hours to minutes: multiply by 60.
- To convert a decimal answer back to hours and minutes: take the decimal part and multiply by 60. For example, 2.35 hours = 2 hours and 0.35 × 60 = 21 minutes.
Worked Example 1 — Foundation Level
A car travels 150 miles in 2 hours 30 minutes. What is the average speed?
Step 1: Convert time to hours: 2 hours 30 minutes = 2.5 hours.
Step 2: Use the formula: Speed = Distance ÷ Time.
Step 3: Speed = 150 ÷ 2.5 = 60 mph.
Worked Example 2 — Higher Level
Priya drives from Town A to Town B at 50 mph. The distance is 80 miles. She then drives from Town B to Town C, a distance of 60 miles, at 40 mph. What is her average speed for the entire journey?
Step 1: Find the time for each stage.
- A to B: Time = 80 ÷ 50 = 1.6 hours.
- B to C: Time = 60 ÷ 40 = 1.5 hours.
Step 2: Find the totals.
- Total distance = 80 + 60 = 140 miles.
- Total time = 1.6 + 1.5 = 3.1 hours.
Step 3: Average speed = Total distance ÷ Total time = 140 ÷ 3.1 = 45.2 mph (1 d.p.).
Important: The average speed is not (50 + 40) ÷ 2 = 45. You must use total distance ÷ total time.
Common Mistakes
- Averaging speeds. Students add the two speeds and divide by two. This only works if the same time is spent at each speed, which is rarely the case.
- Mixing units. Using minutes when the speed is in "per hour" without converting. Always check before substituting.
- Writing time as a decimal incorrectly. 1 hour 20 minutes is 1.333… hours, not 1.20 hours.
- Forgetting to convert the answer back. If the question asks for time in hours and minutes, do not leave 2.75 hours — write 2 hours 45 minutes.
- Not showing units in the answer. Speed has compound units (e.g. mph). Leaving them off can cost marks.
Exam Tips
- Write the formula first — this often earns a method mark even if you make an arithmetic slip.
- Use neat working. In multi-stage problems, set out each stage clearly with labelled calculations.
- Distance–time graphs sometimes appear alongside these questions. The gradient of a straight-line section gives the speed.
- For reverse questions (given speed and time, find distance), multiply rather than divide — double-check you have rearranged correctly.
- Estimate to check. If a car travels 200 miles in 4 hours, the speed should be around 50 mph. If your answer says 500, something has gone wrong.
Practice Questions
Question 1 (Foundation) A cyclist rides 36 km in 1 hour 30 minutes. What is the cyclist's average speed in km/h?
Question 2 (Foundation) A train travels at 90 mph. How far does it travel in 2 hours 20 minutes?
Question 3 (Higher) Ravi walks 3 km at 5 km/h and then runs 7 km at 10 km/h. Find his average speed for the whole journey.
Question 4 (Higher) A car drives at 60 km/h for 45 minutes, rests for 15 minutes, then drives at 80 km/h for 1 hour 30 minutes. Calculate the average speed for the entire journey, including the rest.
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Related Topics
- Compound Measures — density and pressure use the same formula structure
- Unit Conversions — essential for getting units to match
- Distance–Time and Velocity–Time Graphs — graphical interpretation of speed
- Ratio and Proportion — proportional reasoning supports these calculations
Summary
Speed, distance and time are connected by the formula Speed = Distance ÷ Time. Always check that your units are consistent before substituting. For multi-stage journeys, find the total distance and total time before calculating average speed — never simply average the individual speeds. Convert minutes to hours by dividing by 60, and remember to give final answers in the units the question requires. These questions are among the most predictable in the exam, so mastering the method is well worth the effort.