Speed, Distance & Time
Using the speed-distance-time triangle to solve problems involving journeys and rates.
What is Speed, Distance & Time?
Speed, distance and time are connected by three formulae: Speed = Distance / Time, Distance = Speed x Time, Time = Distance / Speed. The “SDT triangle” is a helpful way to remember all three.
In the 11+ exam, these questions often appear as word problems about journeys, trains, cyclists or runners.
Step-by-Step Method
Draw the SDT triangle
Put D at the top, S and T at the bottom. Cover the one you want to find: D/T = S, S x T = D, D/S = T.
Identify what you know and what you need
Read the question to find which two values are given and which one you need to calculate.
Check the units match
If speed is in km/h, distance must be in km and time in hours. Convert if necessary.
Convert minutes to hours if needed
30 minutes = 0.5 hours, 45 minutes = 0.75 hours, 15 minutes = 0.25 hours.
Calculate and check your answer is sensible
A car travelling at 60 mph for 2 hours covers 120 miles – does your answer seem reasonable?
Worked Examples
A car travels 150 km in 3 hours. What is its speed?
Working
- Speed = Distance / Time.
- Speed = 150 / 3 = 50 km/h.
A train travels at 80 mph for 2.5 hours. How far does it go?
Working
- Distance = Speed x Time.
- Distance = 80 x 2.5 = 200 miles.
A cyclist covers 30 km at 12 km/h. How long does it take?
Working
- Time = Distance / Speed.
- Time = 30 / 12 = 2.5 hours.
- 2.5 hours = 2 hours 30 minutes.
Common Mistakes
Mixing up the formulae (e.g. multiplying when you should divide).
Use the SDT triangle: cover what you need to find, and the remaining two show you the operation.
Forgetting to convert minutes to hours.
2 hours 30 minutes is 2.5 hours, not 2.3 hours. Divide the minutes by 60.
Confusing average speed with just adding speeds together.
Average speed = total distance / total time, not the average of two speeds.
Top Tips
- Draw the SDT triangle at the start of every speed/distance/time question.
- Common time conversions: 15 min = 0.25 h, 30 min = 0.5 h, 45 min = 0.75 h.
- For average speed questions, add up ALL the distance and ALL the time first.
- Check your answer makes sense – a walking speed of 100 km/h is clearly wrong!
Ready to practise?
Put these techniques into action with our free practice papers.
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