203k views
1 vote
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

User Sharshi
by
8.8k points

1 Answer

4 votes
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.
User Ddso
by
8.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories