Question

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?

• A. $\frac{3}{4}$hr.
• B. $\frac{11}{2}$hr.
• C. $2hr$.
• D. $\frac{12}{5}$hr.
• E. $\frac{21}{2}$hr.

Answer 1

The correct option is D $\frac{12}{5}$hr.

Let h be the height of the candle
speed of First Candle = $\frac{h}{4}$
speed of Second Candle = $\frac{h}{3}$
how many hours after being lit was the first candle twice the height of the second?
let r be the height of the second candle at that time (t).
$r=h-\left(\frac{h}{3}\right)t$
at the same time(t), the height of the first candle must be 2r
$2r=h-\left(\frac{h}{4}\right)t$
$2(h-(\frac{h}{3}\left)t\right)=h-\left(\frac{h}{4}\right)t$
$2h-\left(\frac{2}{3}\right)ht=h-\left(\frac{1}{4}\right)h$
$2-\left(\frac{2}{3}\right)t=1-\left(\frac{1}{4}\right)t$
$t(\frac{2}{3}-\frac{1}{4})=1$
$t=\frac{12}{5}hror2.4hr$.

so option $D$ is correct answer.