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NSW Y8 Maths

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Pythagoras Working with Numbers Algebra Equations Geometry Area and Perimeter Volume Fractions and Percentages Investigating Data Congruent Figures Probability Rates and Ratios Graphing Linear Equations Time and Travel

NSW Y8 Maths Rates and Ratios Rate Problems

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Rate Problems Theory

\begin{multicols}{2} \textbf{Example 1}\\ An aircraft travelled at \(800 \text{~km} / \text{h}\). How far did it travel in 6 minutes?\\ \textbf{Example 1 solution}\\ In 1 hour \(=800 \text{~km}\)\\ \(\begin{aligned} 60 \text { minutes } & =800 \text{~km} \\ 1 \text { minute } & =\frac{800}{60} \\ 6 \text { minutes } & =\frac{6 \times 800}{60} \\ & =80 \text{~km}. \end{aligned}\) \columnbreak \textbf{Example 2}\\ Smokers lose approximately \(2 \%\) of their lung capacity per year. If Helen with \(100 \%\) lung capacity started smoking at 21 years of age, at what age will she have \(50 \%\) lung capacity left?\\ \textbf{Example 2 solution}\\ Loss of lung capacity per year \(=2 \%\)\\ \(\begin{aligned} \therefore 50 \% \text { loss } & =\frac{50}{2} \\ & =25 \text { years. } \end{aligned}\)\\ \(\therefore\) After 25 years, \(50 \%\) loss.\\ \(\begin{aligned} \text { Helen's age } & =21+25 \\ & =46 \text { years. } \end{aligned}\) \end{multicols}

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