Question

Two pools are leaking After 15 minutes pool A has leaked 2/3 gallon After 20 minutes pool B has 3/4 gallon Which pool is leaking faster

Answer 1

So, after 15 minutes A has leaked 2/3 of a gallon, how much will it be for 20 minutes?  let's see.

$\bf \begin{array}{ccll} minutes&gallons\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 15&\frac{2}{3}\\\\ 20&g \end{array}\implies \cfrac{15}{20}=\cfrac{\frac{2}{3}}{g}\implies \cfrac{15}{20}=\cfrac{\frac{2}{3}}{\frac{g}{1}}\implies \cfrac{3}{4}=\cfrac{2}{3}\cdot \cfrac{1}{g} \\\\\\ \cfrac{3}{4}=\cfrac{2}{3g}\implies 9g=8\implies g=\cfrac{8}{9}$

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.

$\bf \cfrac{3}{4}\cdot \cfrac{9}{9}\implies \boxed{\cfrac{27}{36}} \qquad \qquad \qquad \qquad \qquad \cfrac{8}{9}\cdot \cfrac{4}{4}\implies \boxed{\cfrac{32}{36}}$

so, which one do you think is larger?  well, that is the one that's leaking faster, because is leaking more gallons per minute.