Use rates and unit conversions to solve practical problems including fuel consumption, dosage, power consumption and energy efficiency

What this dot point is asking

NESA wants you to compute rates, use the unitary method to solve worded rate problems, convert between metric units, and apply rates to everyday Australian contexts including fuel consumption, energy use and medication dosages.

The answer

What a rate is

A rate compares two quantities with different units, expressed per single unit of the denominator.

• IMATH_5 km/h: a speed.
• IMATH_6 L per $100$ km: fuel consumption.
• IMATH_8 1.92$/L: unit cost.
• IMATH_9 mg per kg per day: a dosage rate.

A rate is a fraction with units on both top and bottom.

The unitary method

To solve "if $a$ produces $b$, how much does $c$ produce", scale by the ratio $\frac{c}{a}$:

Equivalently, find the value for $1$ unit, then multiply by $c$.

Example: if $5$ kg of meat costs \84$, then$1$kg costs$\\frac{84}{5} = \16.80$, and$8$kg costs$\16.80 \times 8 = \134.40$.

Metric conversions

Divide to go the other way. For area, the factor is squared (1 m$^2$ = $10000$ cm$^2$); for volume it is cubed (1 m$^3$ = $1000$ L).

Fuel consumption

Standard Australian unit: litres per $100$ km. Smaller is better.

To find fuel used for a trip of $d$ km at consumption $c$ L per $100$ km:

Then cost is fuel times price per litre.

Energy use (kWh)

Household electricity is billed in kilowatt-hours (kWh). One kWh is the energy used by a $1000$ watt appliance running for $1$ hour.

For an appliance rated $P$ watts running $t$ hours:

Cost is energy times price per kWh.

Dosage calculations

For weight-based dosing: total dose = (mg per kg) $\times$ patient weight (kg).

Number of tablets or doses: total dose divided by strength per tablet.

Always sanity-check: if a patient ends up taking $100$ tablets a day, you have made a unit error.