EST. 2024 · LONDON·MMXXVI SPECIFICATION
AQA·Edexcel·OCR|Foundation + Higher
Ratio

Sheet № 39 · Foundation + Higher · AQA · Edexcel · OCR

39

Speed, Distance and Time –

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 cor

§Key definitions

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.

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.

Important:

The average speed is not (50 + 40) ÷ 2 = 45. You must use total distance ÷ total time.

§Formulas to memorise

\text{Speed} = \frac{\text{Distance}}{\text{Time}}

\text{Distance} = \text{Speed} \times \text{Time}

\text{Time} = \frac{\text{Distance}}{\text{Speed}}

\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}

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.

Read the question carefully — and identify which quantity you need to find (speed, distance, or time).

Write down the formula — you need.

Minutes to hours: divide by 60. For example, 45 minutes = 45 ÷ 60 = 0.75 hours.

Worked example

See example below.

A car travels 150 miles in 2 hours 30 minutes. What is the average speed?

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.
MMXXVI specification · AQA · Edexcel · OCRgcsemathsai.co.uk/formulas/speed-distance-and-time