Question

The time required for an outlet pipe to an empty a tank is inversely proportional to the cross-sectional area of the pipe. A pipe with the cross-sectional area of 113.0 square inches requires 6.4 hours to empty a certain tank if the pipe was replaced with one with a cross-sectional area of 50.25 square inches, how long would it take to empty the same tank

Answer 1

$\bf \qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------$

$\bf \stackrel{\textit{\underline{t}ime to empty a tank is inversely proportional to \underline{c}ross-sectional area}}{t=\cfrac{k}{c}} \\\\\\ \textit{we also know that } \begin{cases} c=113.0\\ t=6.4 \end{cases}\implies 6.4=\cfrac{k}{113}\implies 723.2=k \\\\\\ therefore\qquad \boxed{t=\cfrac{723.2}{c}} \\\\\\ \textit{when c = 50.25, what is \underline{t}?}\qquad t=\cfrac{723.2}{50.25}\implies t\approx 14.3920398$