Two types of candles have the same length but are made of different materials. One of them burns completely in three hours, and the other in four hours, both burning at a uniform rate. How many minutes after 1 PM should the two candles be lit simultaneously so that, at 4 PM, the length of one is double that of the other?
(a) 24
(b) 28
(c) 36
(d) 40
(e) 48
The correct option is (c).

Since the actual length of the candles is irrelevant, we can assume any size for the candles, and the answer will always be the same. The simplest is to assume that both candles have a length of one unit. Thus, the one that burns in 3 hours burns at a constant rate of $1 / 3$ (candle per hour) and the one that burns in 4 hours burns at a rate of $1 / 4$ (candle per hour). Therefore, after some time (in hours) $t$, one burns $t / 3$ (candle) and the other $t / 4$ (candle), so what remains of one candle after time $t$ is $1-t / 3$ and of the other, $1-t / 4$. We want to know how much time elapses from the moment $t=0$ until the length of the candle that burns more slowly is twice the length of the candle that burns more quickly, which is equivalent to solving the equation

$$
1-\frac{t}{4}=2\left(1-\frac{t}{3}\right)=2-\frac{2 t}{3}
$$

Since $\frac{2}{3}-\frac{1}{4}=\frac{5}{12}$, the only solution is $t=\frac{12}{5}=2 \frac{2}{5}$ hours, which is equivalent to 2 hours and 24 minutes. Thus, after 2 hours and 24 minutes, the length of one candle is twice the length of the other. Since we want this to happen at 16:00, the candles should be lit at 13:36.