Speed, Distance & Time Calculations –

Speed, distance and time problems appear on almost every GCSE Maths paper. Whether the question involves a car journey, a runner, or a distance-time graph, the same core formula applies. This guide takes you through the formula triangle, unit conversions, average speed, and how to interpret distance-time graphs, with fully worked examples at both tiers.

What Is the Speed-Distance-Time Relationship?

Speed measures how fast an object is moving. It is calculated by dividing the distance travelled by the time taken. The three quantities — speed, distance, and time — are linked by a single formula that can be rearranged depending on which value you need.

The formula triangle is a useful memory aid. Write D at the top, S at the bottom left and T at the bottom right. Cover the letter you need: if you cover D, you see S × T; cover S, you see D ÷ T; cover T, you see D ÷ S.

Speed is a compound measure because it combines two different units — a unit of distance and a unit of time. Common units include km/h (kilometres per hour), m/s (metres per second) and mph (miles per hour). Matching your units before calculating is essential.

Key Formulas

Step-by-Step Method

1. Identify which quantity you need to find (speed, distance, or time).
2. Check units — make sure distance and time units are consistent with the speed units.
3. Substitute into the correct rearrangement of the formula.
4. Calculate and include the correct unit in your answer.

Worked Example 1 — Foundation Level

Question: A cyclist travels 45 km in 3 hours. What is the cyclist's average speed?

Working: Speed = Distance ÷ Time Speed = 45 ÷ 3 = 15 km/h.

Answer: The average speed is 15 km/h.

Worked Example 2 — Higher Level

Question: A train travels at 90 km/h for 2 hours 20 minutes. How far does it travel?

Working: Convert time to hours: 2 hours 20 minutes = 2 + 20/60 = 2⅓ hours = 7/3 hours. Distance = Speed × Time = 90 × 7/3 = 210 km.

Answer: The train travels 210 km.

Worked Example 3 — Exam Style

Question: Priya drives 120 miles from Leeds to London. She drives the first 60 miles at 40 mph and the remaining 60 miles at 60 mph. Work out her average speed for the whole journey.

Working: Time for first part = 60 ÷ 40 = 1.5 hours. Time for second part = 60 ÷ 60 = 1 hour. Total time = 1.5 + 1 = 2.5 hours. Total distance = 120 miles. Average speed = 120 ÷ 2.5 = 48 mph.

Answer: The average speed is 48 mph. (Note: it is not simply the mean of 40 and 60.)

Common Mistakes

• Averaging the two speeds directly. Average speed = total distance ÷ total time, not the mean of the individual speeds. The worked example above shows why.
• Using minutes instead of hours. If time is given as 2 hours 15 minutes, convert to 2.25 hours before dividing. Do not use 2.15.
• Forgetting unit conversions. If speed is in m/s and distance is in km, convert km to metres first, or convert speed to km/h.

Exam Tips

• Always state the formula you are using — this earns a method mark even if the arithmetic goes wrong.
• On distance-time graph questions, remember that the gradient of a line gives the speed. A steeper line means a faster speed.
• A horizontal section on a distance-time graph means the object is stationary (speed = 0).
• When converting minutes to hours, divide by 60 — not by 100. For example, 45 minutes = 0.75 hours, not 0.45.

Practice Questions

Q1 (Foundation): A runner covers 800 metres in 2 minutes 30 seconds. Calculate the speed in m/s.

Q2 (Foundation): How far does a car travel in 45 minutes at a speed of 60 km/h?

Q3 (Higher): A bus travels 24 km at 32 km/h, then 36 km at 48 km/h. Find the average speed for the whole journey.

Practise speed, distance and time questions with instant feedback — completely free on GCSEMathsAI.

Related Topics

• Speed Distance and Time
• Compound Measures
• Unit Conversions

Summary

• Speed = Distance ÷ Time. Rearrange using the formula triangle for distance or time.
• Always convert time into hours (or seconds) before substituting — do not mix units.
• Average speed is total distance divided by total time, not the mean of individual speeds.
• On distance-time graphs, the gradient represents speed and a flat line means stationary.
• To convert km/h to m/s, divide by 3.6. To convert m/s to km/h, multiply by 3.6.
• Speed is a compound measure — always include the correct compound unit (e.g., km/h, m/s) in your answer.