Question

A broken faucet leaks 1 gallon of water every 1 and1/3 months the amount of months that pass m varies directly with the amount of gallons leaked g. Find the equation that models this direct variation. How many months will it take for the faucet to leak 7 gallons of water?

Answer 1

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

$\bf \textit{\underline{m} varies directly with the amount of gallons}\implies \stackrel{months}{m}=k\stackrel{gallons}{g} \\\\\\ \textit{we also know that } \begin{cases} m=1\frac{1}{3}\\ \qquad \frac{4}{3}\\ g=1 \end{cases}\implies \cfrac{4}{3}=k1\implies \cfrac{4}{3}=k \\\\\\ \boxed{m=\cfrac{4}{3}g}\\\\ -------------------------------\\\\ \textit{what's \underline{m} when g=7?}\qquad m=\cfrac{4}{3}\cdot 7\implies m=\cfrac{28}{3}\implies m=9\frac{1}{3}$