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&(2)/(3)\\\\ 20&g \end{array}\implies \cfrac{15}{20}=\cfrac{(2)/(3)}{g}\implies \cfrac{15}{20}=\cfrac{(2)/(3)}{(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.