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Speed, Distance and Time

FoundationHigherAQAEdexcelOCR

Get to grips with speed, distance and time using these Foundation and Higher GCSE Maths practice questions. The worksheet focuses on speed, distance and time calculations, and the accompanying mark scheme breaks down each solution clearly. Suitable for AQA, Edexcel and OCR. Download the questions and answers for free. Use the formula triangle: speed = distance ÷ time.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

Speed is the distance travelled per unit of time, calculated as \(\text{speed} = \frac{\text{distance}}{\text{time}}\). Common units are metres per second and kilometres per hour.

The formula rearranges to give distance as speed multiplied by time, and time as distance divided by speed. All three forms appear regularly in exam questions.

Units are the main source of error. If the speed is in km/h, the time must be in hours, so \(30\) minutes has to become \(0.5\) hours before you calculate. Converting first, before substituting, avoids the problem entirely.

Revision notes

The formula

\(\text{speed} = \frac{\text{distance}}{\text{time}}\), with distance equal to speed times time.

A journey of \(150\)km in \(3\) hours gives an average speed of \(50\)km/h.

Time conversions

Times in minutes must be converted to hours for km/h, by dividing by \(60\).

So \(45\) minutes is \(0.75\) hours, and \(1\) hour \(30\) minutes is \(1.5\) hours. Writing \(1.30\) for one and a half hours is a frequent and costly error.

Average speed

For a journey in stages, find the total distance and the total time, then divide.

Averaging the individual speeds gives the wrong answer, because the stages usually take different amounts of time.

Key points

  • Speed equals distance divided by time.
  • Distance equals speed times time.
  • Time equals distance divided by speed.
  • Convert minutes to hours for km/h.
  • \(45\) minutes is \(0.75\) hours, not \(0.45\).
  • Average speed uses total distance over total time.

Worked examples

Example 1

A car travels \(180\)km in \(3\) hours. Find its average speed.

Working

\[\frac{180}{3}\]divide distance by time
\[= 60\text{km/h}\]state the speed with units

Example 2

A cyclist travels at \(12\)km/h for \(45\) minutes. Find the distance.

Working

\[45 \text{ minutes} = 0.75 \text{ hours}\]convert the time to hours
\[12 \times 0.75\]distance equals speed times time
\[= 9\text{km}\]state the distance

Example 3

A train covers \(240\)km at \(80\)km/h. Find the time taken.

Working

\[\frac{240}{80}\]time equals distance divided by speed
\[= 3 \text{ hours}\]state the time

Common mistakes

  • Writing 90 minutes as 1.30 hours.

    It is 1.5 hours. Divide the minutes by 60, not by 100.

  • Averaging two speeds directly.

    Average speed is total distance divided by total time, not the mean of the speeds.

  • Mixing units.

    Speed in km/h needs distance in km and time in hours.

  • Omitting units.

    Speed must be given with its compound unit, such as km/h.

Exam tips

  • Convert all times to hours before substituting.
  • Use total distance over total time for average speed.
  • Include the compound unit in every answer.
  • Sense-check whether the answer is a plausible speed.

Key terms

Speed
Distance travelled per unit of time.
Average speed
Total distance divided by total time.
Compound unit
A unit combining two others, such as km/h.
Distance
How far something has travelled.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.