Question

One tank is filling at the rate of 3/4 gallon / 2/3 minute a second tank is filling at the rate of 3/8 gallon per 1/2 minute which tank is filling faster equation

Answer 1

`\bf \cfrac{\quad \stackrel{gallons}{(3)/(4)}\quad }{\stackrel{minutes}{(2)/(3)}}\implies \cfrac{3}{4}\cdot \cfrac{3}{2}\implies \cfrac{9}{8}~g/m \\\\\\ \cfrac{\quad \stackrel{gallons}{(3)/(8)}\quad }{\stackrel{minutes}{(1)/(2)}}\implies \cfrac{3}{8}\cdot \cfrac{2}{1}\implies \cfrac{3}{4}~g/m\\\\ -------------------------------`


`\bf \cfrac{3}{4}\cdot \cfrac{2}{2}\implies \cfrac{6}{8}\quad \textit{clearly then }\cfrac{9}{8}\textit{ is larger than }\cfrac{6}{8} \\\\\\ \stackrel{\stackrel{tank's~volume}{gallons}}{y}=\cfrac{9}{8}\stackrel{minutes}{x}`