Speed, distance and time, explained with examples
Speed tells you how far something travels in a given time. The formula linking speed, distance and time is simple, but GCSE questions test it with awkward units, multi-part journeys and graphs, so careful working matters.
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The formula
speed = distance ÷ time
Rearranged: distance = speed × time and time = distance ÷ speed.
A formula triangle helps you remember all three: put D at the top and S and T side by side underneath. Cover the quantity you want: covering D leaves S × T; covering S leaves D over T; covering T leaves D over S.
The units of speed come from the units of distance and time: kilometres and hours give km/h; metres and seconds give m/s; miles and hours give mph. Always check that the units match before you calculate. If a question gives a distance in metres and a time in minutes, convert one of them first, or your answer will be in an unusual unit that is easy to misread.
Worked examples
Example 1: finding speed
A cyclist travels 36 km in 2 hours. Find the average speed.
- speed = 36 ÷ 2 = 18 km/h.
Example 2: finding distance
A train travels at 120 km/h for 45 minutes. How far does it go?
- Convert the time: 45 minutes = 0.75 hours.
- distance = 120 × 0.75 = 90 km.
Example 3: finding time
A car travels 150 miles at 60 mph. How long does it take, in hours and minutes?
- time = 150 ÷ 60 = 2.5 hours.
- 0.5 hours = 30 minutes, so 2 hours 30 minutes.
Converting times
Time conversions cause more lost marks than anything else in this topic, because time is not decimal. 2.5 hours is 2 hours 30 minutes, not 2 hours 50 minutes. To convert:
- Minutes to hours: divide by 60. 20 minutes = 20/60 = 1/3 hour ≈ 0.333 hours.
- Decimal hours to minutes: multiply the decimal part by 60. 1.2 hours = 1 hour 12 minutes.
- Hours and minutes to hours: 3 hours 15 minutes = 3.25 hours.
Example 4: a decimal answer
A runner covers 10 km at 12 km/h. How long does it take?
- time = 10 ÷ 12 = 0.8333… hours.
- 0.8333 × 60 = 50 minutes. 50 minutes.
Converting speeds
To change km/h to m/s, convert both parts: multiply by 1000 to get metres, and divide by 3600 to get seconds. That is the same as dividing by 3.6. To go from m/s to km/h, multiply by 3.6.
Example 5: km/h to m/s
Convert 90 km/h to m/s.
- 90 × 1000 = 90,000 m per hour. 90,000 ÷ 3600 = 25.
- 25 m/s, or simply 90 ÷ 3.6.
Average speed for a journey in parts
Average speed is total distance divided by total time. It is not the average of the speeds, unless each part takes the same time. This is a favourite exam trap.
Example 6: two-part journey
A driver travels 60 km at 30 km/h and then 60 km at 60 km/h. Find the average speed for the whole journey.
- Time for part 1: 60/30 = 2 hours. Part 2: 60/60 = 1 hour.
- Total distance 120 km, total time 3 hours, so average speed = 40 km/h.
- Averaging the two speeds would give 45 km/h, which is wrong, because more time was spent at the slower speed.
Example 7: including a stop
A delivery van travels 40 miles in 1 hour, stops for 30 minutes, then travels 50 miles in 1.5 hours. Find its average speed for the whole trip.
- Total distance = 90 miles. Total time = 1 + 0.5 + 1.5 = 3 hours, including the stop.
- Average speed = 30 mph.
Example 8: two objects meeting
Two trains start 150 km apart and travel towards each other, one at 70 km/h and the other at 80 km/h. How long until they meet?
- Moving towards each other, they close the gap at a combined 70 + 80 = 150 km/h.
- Time = 150 ÷ 150 = 1 hour. Adding speeds for objects approaching each other is a neat shortcut.
Example 9: speed with bounds (Higher)
A runner covers 100 m, measured to the nearest metre, in 12.4 s, to the nearest 0.1 s. Find the upper bound of the runner's speed.
- Maximum speed = maximum distance ÷ minimum time = 100.5 ÷ 12.35.
- ≈ 8.14 m/s. To make a quotient as large as possible, divide the largest top by the smallest bottom.
Distance-time graphs
On a distance-time graph:
- the gradient (steepness) is the speed;
- a horizontal line means the object is stationary;
- a steeper line means a faster speed;
- a line sloping back down towards the axis means the object is returning towards the start.
Example 10: reading a graph
On a distance-time graph, a line goes from (0, 0) to (2 hours, 50 km), stays flat until 3 hours, then rises to 80 km at 3.5 hours. Describe the journey and find each speed.
- First stage: 50 km in 2 hours, so 25 km/h.
- Flat from 2 to 3 hours: stopped for 1 hour.
- Last stage: 30 km in 0.5 hours, so 60 km/h, the fastest part.
Related compound measures
Speed is a compound measure, made by combining two other measures. GCSE also uses density (mass ÷ volume) and pressure (force ÷ area), and the same triangle method and unit care apply to all of them. In every case, write the formula, convert units, substitute, and finish with the correct compound unit, such as g/cm³ for density or N/m² for pressure.
Common mistakes
- Treating 1.5 hours as 1 hour 50 minutes.
- Mixing units, such as speed in km/h with time in minutes.
- Averaging speeds instead of dividing total distance by total time.
- Forgetting to include stops in the total time for average speed.
Practice questions
Try each one before opening the answer.
Q1. A plane flies 2400 km in 3 hours. Find its average speed.
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Q2. How far does a car go in 2 hours 15 minutes at 48 mph?
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Q3. Convert 15 m/s to km/h.
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Q4. A walker goes 6 km at 4 km/h, then 6 km at 6 km/h. Find the average speed.
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Frequently asked questions
Is speed, distance and time on GCSE Maths Foundation?
Yes. Compound measures, including speed, are on both tiers. Higher papers add harder unit conversions and links to graphs and bounds.
Is speed the same as velocity?
Not quite. Speed is how fast; velocity is speed in a given direction. GCSE Physics uses velocity for motion graphs and vectors.
Key takeaways
- speed = distance ÷ time; use the D-S-T triangle.
- Match units before calculating.
- Convert minutes to hours by dividing by 60.
- km/h ÷ 3.6 = m/s.
- Average speed = total distance ÷ total time, including stops.