so, after 15 minutes A has leaked 2/3 of a gallon, how much will it be for 20 minutes? let's see.
[tex]\bf \begin{array}{ccll}
minutes&gallons\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
15&\frac{2}{3}\\\\
20&g
\end{array}\implies \cfrac{15}{20}=\cfrac{\frac{2}{3}}{g}\implies \cfrac{15}{20}=\cfrac{\frac{2}{3}}{\frac{g}{1}}\implies \cfrac{3}{4}=\cfrac{2}{3}\cdot \cfrac{1}{g}
\\\\\\
\cfrac{3}{4}=\cfrac{2}{3g}\implies 9g=8\implies g=\cfrac{8}{9}[/tex]
so in 20 minutes A has leaked that much, which is larger, 8/9 or 3/4?
let's multiply each fraction by "the other's denominator", to make them the same denominator.
[tex]\bf \cfrac{3}{4}\cdot \cfrac{9}{9}\implies \boxed{\cfrac{27}{36}}
\qquad \qquad \qquad \qquad \qquad
\cfrac{8}{9}\cdot \cfrac{4}{4}\implies \boxed{\cfrac{32}{36}}
[/tex]
so, which one do you think is larger? well, that is the one that's leaking faster, because is leaking more gallons per minute.
