Question

Hey cylindrical water tank is being filled with the hose. The depth of the water increases by 1 1/4 ft./h how many hours will it take for the water level in the tank to be 3 1/2 feet depth. The answer must be in a mixed number form.

Answer 1

First off, let's convert the mixed fractions to "improper", keeping in mind that the water is increasing every passing hour by 1 and 1/4.

$\bf \stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}} \\\\\\ \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}\\\\ -------------------------------$

$\bf \begin{array}{ccll} feet&hours\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{5}{4}&1\\\\ \frac{7}{2}&h \end{array}\implies \cfrac{\quad \frac{5}{4}\quad }{\frac{7}{2}}=\cfrac{1}{h}\implies \cfrac{5}{4}\cdot \cfrac{2}{7}=\cfrac{1}{h}\implies \cfrac{5}{2}\cdot \cfrac{1}{7}=\cfrac{1}{h} \\\\\\ \cfrac{5}{14}=\cfrac{1}{h}\implies h=\cfrac{14\cdot 1}{5}\implies h=\cfrac{14}{5}\implies h=2\frac{4}{5}$