[tex]\bf \qquad \qquad \textit{double proportional variation}\\\\
\begin{array}{llll}
\textit{\underline{y} varies directly with \underline{x}}\\
\textit{and inversely with \underline{z}}
\end{array}\implies y=\cfrac{kx}{z}\impliedby
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------\\\\
\textit{\underline{r} varies directly as \underline{s} and inversely as \underline{t} cubed}\qquad r=\cfrac{ks}{t^3}[/tex]
[tex]\bf \textit{we also know that }
\begin{cases}
r=607.5\\
s=12\\
t=2
\end{cases}\implies 607.5=\cfrac{k12}{2^3}
\\\\\\
607.5=\cfrac{12k}{8}\implies 607.5=\cfrac{3k}{2}\implies \cfrac{607.5\cdot 2}{3}=k\implies 405=k
\\\\\\
therefore\qquad \boxed{r=\cfrac{405s}{t^3}}
\\\\\\
\textit{now, when s = 42 and t = 6, what is \underline{r}?}\qquad r=\cfrac{405(42)}{6^3}[/tex]
