Math Artifacts

$$\text{Only Time Candle}$$

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Diwali is the festival of lights. Celebrations are filled with fireworks, diyas, and candles, creating stunning designs. You are designing a rangoli and want to use three candles of different sizes. You know that each size of candle has a different burning time, the small ones will burn for exactly $1$ hour, medium for exactly $3$ hours, and the large for exactly $4$ hours, but they do not burn at constant rates.

You could measure $5$ hours exactly by first burning the $1$ hour candle, and then burning the $4$ hour candle as soon as the $1$ hour candle finishes. However, you could not burn the $4$ hour candle halfway to measure $2$ hours, because you would not know where halfway is, since the candle doesn't burn at a constant rate.