Rates and unit conversion

A rate compares a quantity with one unit of another quantity. Its units show the division: cost per kilogram, litres per minute, or grams per cubic centimetre. Multiply a constant rate by the amount of the denominator quantity to recover the total.

Example

A tap delivers \(18\) litres in \(45\) seconds at a constant rate. Its rate is \(\dfrac{18}{45}=0.4\text{ litre/s}=24\text{ litres/min}\). In \(2.5\) minutes it delivers \(60\) litres.

\(72\text{ km/h}=72\times\dfrac{1000}{3600}=20\text{ m/s}\). Thus divide by \(3.6\) to change km/h to m/s; multiply by \(3.6\) for the reverse conversion.

Convert \(1\text{ h}\hspace{0.5em}24\text{ min}\) to \(1+\dfrac{24}{60}=1.4\text{ h}\), not \(1.24\text{ h}\).