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

  • $\mathrm{Speed}=\frac{\mathrm{Distance}}{\mathrm{Time}}$

  • 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

  • $\mathrm{Density}=\frac{\mathrm{Mass}}{\mathrm{Volume}}$

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

• Fuel consumption is equal to distance divided by fuel used

  • $\mathrm{Fuel}\mathrm{consumption}=\frac{\mathrm{Distance}}{\mathrm{Fuel}\mathrm{used}}$

  • 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

    • $\mathrm{Fuel}\mathrm{consumption}=\frac{\mathrm{Distance}}{\mathrm{Fuel}\mathrm{used}}$

    • $40=\frac{100}{\mathrm{Fuel}\mathrm{used}}$

  • Multiply both sides by "fuel used"

    • $40\times \mathrm{Fuel}\mathrm{used}=100$

  • Divide both sides by 40

    • $\mathrm{Fuel}\mathrm{used}=\frac{100}{40}=2.5\mathrm{gallons}$

  • 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

    • $\frac{\mathrm{kg}}{{\mathrm{cm}}^3}\times {\mathrm{cm}}^3=\mathrm{kg}$