Question

In a fireplace, about 3/4 of an 18 inch log will burn in 1/3 of an hour. How many hours will it take to burn 2 1/2 logs

Answer 1

$\bf \begin{array}{ccll} \stackrel{burned}{log}&\stackrel{time}{hr}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{3}{4}&\frac{1}{3}\\\\ 2\frac{1}{2}&h \end{array}\implies \cfrac{\frac{3}{4}}{2\frac{1}{2}}=\cfrac{\frac{1}{3}}{h}\implies \cfrac{\frac{3}{4}}{\frac{2\cdot 2+1}{2}}=\cfrac{\frac{1}{3}}{\frac{h}{1}}$

$\bf \cfrac{\frac{3}{4}}{\frac{5}{2}}=\cfrac{1}{3}\cdot \cfrac{1}{h}\implies \cfrac{3}{4}\cdot \cfrac{2}{5}=\cfrac{1}{3h}\implies \cfrac{6}{20}=\cfrac{1}{3h}\implies 6\cdot 3h=20\cdot 1 \\\\\\ 18h=20\implies h=\cfrac{20}{18}\implies h=\cfrac{10}{9}\implies h=1\frac{1}{9}$

about 1 hour and 6 minutes with 36 seconds.