Question

The time, T (seconds) it takes for a pot of water to boil is inversely proportional to the cooker setting, H , applied to the pot. When H = 7 , T = 90 . Work out T when H = 3

Answer 1

`\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill`

`\stackrel{\textit{T varies inversely with H}}{T = \cfrac{k}{H}}\hspace{5em}\textit{we also know that} \begin{cases} H=7\\ T=90 \end{cases} \\\\\\ 90=\cfrac{k}{7}\implies 630=k\hspace{5em}\boxed{T=\cfrac{630}{H}} \\\\\\ \textit{when H = 3, what's`