Time and speed problems are almost always solved by the same triangle. Once your child knows it, these questions turn into some of the fastest, most reliable marks on the whole paper. The catch is never the arithmetic itself. It is the units, the clock arithmetic and the last sentence of the worded problem quietly changing what is being asked. This guide walks through the method, the exam traps and the mental shortcuts that turn a slow, error-prone question into a ten-second win.
The speed-distance-time triangle
Draw a triangle. Put D (distance) in the top box, and S (speed) and T (time) in the two bottom boxes. Cover the value you want with a finger, and the other two show you exactly what to do. This one picture handles every version of the question.
- Want distance? Cover D. You see S next to T, so multiply: Distance = Speed × Time.
- Want speed? Cover S. You see D above T, so divide: Speed = Distance ÷ Time.
- Want time? Cover T. You see D above S, so divide: Time = Distance ÷ Speed.
The word "per" is your clue that a rate is involved. Miles per hour, metres per second, cost per kilogram. The unit before "per" goes on top, the unit after goes on the bottom, and the triangle sorts out the rest.
Watch the units first, always
This is where most marks are lost. If speed is given in kilometres per hour but the time is given in minutes, you cannot just multiply. Convert one of them so they match before you touch the triangle. A car travelling at 60 km/h for 30 minutes covers 30 km, not 1,800 km, because 30 minutes is half an hour.
Keep these conversions ready. In a GL-style paper you cannot use a calculator, so speed and accuracy on these matters more than the "hard" maths that follows.
| You have | You want | Do this |
|---|---|---|
| Minutes | Hours | Divide by 60 (45 min = 0.75 h) |
| Hours | Minutes | Multiply by 60 (1.5 h = 90 min) |
| Kilometres | Metres | Multiply by 1,000 |
| km/h | m/s | Multiply by 1,000, divide by 3,600 |
A quick trap: half an hour is 0.5, not 0.30. A common wrong answer treats "30 minutes" as 0.30 hours. Because it is genuinely 0.5 hours, every answer built on 0.30 is wrong. Our free worksheets drill these conversions until they are automatic.
A full worked example
A cyclist rides 24 kilometres in 1 hour 30 minutes. What is her average speed in km/h?
- Underline the question. It wants speed in km/h, so time must be in hours.
- Convert. 1 hour 30 minutes = 1.5 hours.
- Cover S in the triangle. Speed = Distance ÷ Time = 24 ÷ 1.5.
- Calculate. 24 ÷ 1.5 = 16. Her average speed is 16 km/h.
In a GL multiple-choice paper this would appear with five options (A to E) on a separate OMR answer sheet. Distractors are chosen on purpose: 24 ÷ 1.30 gives a messy decimal, and 24 × 1.5 gives 36. Both "wrong" answers are usually sitting there waiting for a rushed child.
Clock arithmetic: split, never lump
Many 11+ questions hide the maths inside a timetable: "A train leaves at 09:45 and the journey lasts 2 hours 35 minutes. When does it arrive?" Do not try to add it all in one go. Split it:
- 09:45 + 2 hours = 11:45
- 11:45 + 35 minutes = 12:20
The arrival time is 12:20. When the minutes push past 60, add the extra as an hour: 11:45 + 35 minutes crosses the hour, so 45 + 35 = 80 minutes = 1 hour 20 minutes. Remember there is no "10:60" — sixty minutes is the next hour. Timetables and 24-hour clocks appear across GL, CSSE and independent papers, so build fluency early with the revision hub.
Quick-reference formula box
| Find | Formula |
|---|---|
| Distance | Speed × Time |
| Speed | Distance ÷ Time |
| Time | Distance ÷ Speed |
| Average speed | Total distance ÷ total time |
Note that "average speed" means total distance over total time — you cannot simply average two speeds. If a child drives 30 km at 60 km/h and 30 km at 30 km/h, the average speed is not 45 km/h, because more time is spent on the slower half.
Difficulty progression by year group
Building the skill in stages keeps it achievable. A realistic timeline looks like this:
- Year 4: read clocks confidently, work out simple elapsed time, and grasp "per hour" as a rate.
- Year 5: use the triangle with whole-number values and single-step conversions (minutes to hours).
- Year 6: multi-step problems, average speed, and mixed units under exam timing of roughly a minute a question.
Time yourself against a paper on the mock papers page, and check which regional board your target schools use through the grammar school directory and GL papers guide.
Exam traps that cost marks
- Mismatched units — minutes with km/h. Convert first, every time.
- Treating 30 minutes as 0.30 hours instead of 0.5.
- Answering the wrong quantity because the final sentence flipped from "how far" to "how long".
- Averaging two speeds directly instead of using total distance over total time.
- Forgetting a journey that crosses midday or midnight on a 24-hour clock.
Frequently asked questions
Is a calculator allowed in the 11+?
No. GL and most 11+ papers are non-calculator, so children must be fluent with dividing by 1.5, halving and doubling, and converting minutes to hours in their heads.
How is the score reported?
Raw marks are converted to a Standard Age Score (roughly 69 to 141, with 100 as average), which adjusts for a child's age in months. Many grammar schools look for about 111 or higher, though exact marks vary by area and year.
How much time should my child spend per question?
In a 50-question, 50-minute GL paper the target is about one minute each. Speed-distance-time questions should take well under that once the triangle is second nature.