Speed, Density & Fuel Consumption (WJEC GCSE Maths & Numeracy (Double Award)): Revision Note

Speed, Density & Fuel Consumption

What are speed, density and fuel consumption?

• Speed, density and fuel consumption are frequently used compound measures

• Speed is equal to distance divided by time

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  • E.g. Metres per second (m/s), kilometres per hour (km/h) or miles per hour (mph)

• Density is equal to mass divided by volume

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  • E.g. Kilograms per m³ (kg/m³) or grams per cm³ (g/cm³)

• Fuel consumption is equal to distance divided by fuel used

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  • E.g. Miles per gallon (mpg), or Kilometres per litre (km/l)

• You need to be able to rearrange each of these equations to find a missing value

  • E.g. To find the fuel used by a car which has a fuel consumption of 40 mpg travelling 100 miles

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  • Multiply both sides by "fuel used"

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  • Divide both sides by 40

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  • You could instead rearrange the formula before substituting the values in

What if there is a mixture of units?

• If there is a mixture of units given for a quantity, you need to convert them so that they match

• For example

  • Time could be given in a mixture of hours, minutes, and seconds

  • Mass could be given in a mixture of grams and kilograms

  • Distance could be given in a mixture of kilometres and metres

• Convert them all to the same unit before calculating

• Make sure your units match between quantities too

  • E.g. If fuel consumption is in kilometres per litre, the distance should be in kilometres, not metres

• Always check the units used in your calculation to determine the units for your answer

  • E.g. kilograms per cm³ multiplied by cm³ will give an answer in kilograms

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