Question

Candy has to paint a fence. If she can paint 2/3 of the section in 1/2 an hour, and there are 9 sections, how long will it take her to paint the entire fence?

Answer 1

The answer is 45min or 3/4 of an hour

Answer 2

$\bf \begin{array}{ccll} section&hours\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{2}{3}&\frac{1}{2}\\\\ 9&h \end{array}\implies \cfrac{\quad \frac{2}{3}\quad }{9}=\cfrac{\quad \frac{1}{2}\quad }{h}\implies \cfrac{\quad \frac{2}{3}\quad }{\frac{9}{1}}=\cfrac{\quad \frac{1}{2}\quad }{\frac{h}{1}} \\\\\\ \cfrac{2}{3}\cdot \cfrac{1}{9}=\cfrac{1}{2}\cdot \cfrac{1}{h}\implies \cfrac{2}{27}=\cfrac{1}{2h}\implies 4h=27\implies h=\cfrac{27}{4}\implies h=6\frac{3}{4}$