the time it takes to fill a water tank varies inversely with the water rate of the hose. At 8 gallons per minute, a hose can fill the tank in 45 minutes. How long will it take to fill the same tank at 15 gallons per minute
Accepted Solution
A:
[tex]\bf \qquad \qquad \textit{inverse proportional variation}\\\\
\textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------\\\\
\textit{time it takes to fill a tank varies inversely with the water rate}\\\\
t=\cfrac{k}{w}\quad
\begin{cases}
t=\textit{time to fill}\\
w=\textit{water rate}
\end{cases}[/tex]
[tex]\bf \textit{we also know that }
\begin{cases}
w=\stackrel{g/min}{8}\\
t=\stackrel{min}{45}
\end{cases}\implies 45=\cfrac{k}{8}\implies 360=k
\\\\\\
therefore\qquad \boxed{t=\cfrac{360}{w}}
\\\\\\
\textit{now if w = 15, what is \underline{t}?}\qquad t=\cfrac{360}{15}[/tex]