Question

The time it takes to travel between two towns varies inversely as the speed. if it takes marta 3 hours to travel from her house to her sister's house at 45 mph, what is the constant variation?

Answer 1

`\bf \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 } \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{\underline{t}ime varies inversely with \underline{s}peed}}{t = \cfrac{k}{s}}\qquad \textit{we know that } \begin{cases} t = \stackrel{hours}{3}\\ s = \stackrel{mph}{45} \end{cases} \\\\\\ 3=\cfrac{k}{45}\implies 135=k`