Question

Peyton ran 4/5 of a mile in 1/8 of an hour . What is peyton's constant of proportionality in miles per hour?

Answer 1

now, we're assuming they're directly proportional, so say y = miles, x = hours.

$\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we know that } \begin{cases} y=\frac{4}{5}\\[0.8em] x=\frac{1}{8} \end{cases}\implies \cfrac{4}{5}=k\cfrac{1}{8}\implies \cfrac{4}{5}=\cfrac{k}{8} \\\\\\ \cfrac{8\cdot 4}{5}=k\implies \cfrac{32}{5}=k\implies 6\frac{2}{5}=k$