1956 AHSME Problems/Problem 19

Problem 19

Two candles of the same height are lighted at the same time. The first is consumed in $4$ hours and the second in $3$ hours. Assuming that each candle burns at a constant rate, in how many hours after being lighted was the first candle twice the height of the second?

$\textbf{(A)}\ \frac{3}{4}\qquad\textbf{(B)}\ 1\frac{1}{2}\qquad\textbf{(C)}\ 2\qquad\textbf{(D)}\ 2\frac{2}{5}\qquad\textbf{(E)}\ 2\frac{1}{2}$

Solution

In $x$ hours, the height of the first candle is $4-x$ and the height of the second candle is $3-x.$ Essentially, we are solving the equation $4-x = 2(3-x).$ This happens after $x = \boxed{\textbf{(C)} \quad 2}$ hours.

~coolmath34

1956 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 18	Followed by Problem 20
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1956 AHSME Problems/Problem 19

Problem 19

Solution

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