Candelas

We burned two candles of different thickness and length. The longer one burnt for three and a half hours and the shorter one for five hours. After two hours of burning, they were the same height. How many times was the longer candle originally taller than the shorter candle?

Final Answer:

x =  1.4

Step-by-step explanation:

$$\begin{gathered} t_1=3.5\text{h} \\ {t}_2=5\text{h} \\ t=2\text{h} \\ a-\frac{t}{3.5}\cdot a=b-\frac{t}{5}\cdot b \\ a(1-\frac{2}{3.5})=b(1-\frac{2}{5}) \\ x=a/b \\ x=\frac{1-\frac{t}{t_2}}{1-\frac{t}{t_1}}=\frac{1-\frac{2}{5}}{1-\frac{2}{3.5}}=\frac{7}{5}=1\frac{2}{5}=1.4 \end{gathered}$$

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