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Melting Candles
There are two candles of equal lengths but different thickness. The thicker candle lasts for six hours, while the thinner candle lasts for four hours. A person lights the two candles at the same time and then leaves. After returning home, the person saw that the thicker candle was twice the length of thinner one.
How long ago did the person light the two candles?
Hint
When answering these types of questions, remember that they are likely to be answered without the use of a calculator. The answer will likely be a whole number between one and six.
Solution
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**Solution: Three Hours** The thicker candle has a total burning time of 6 hours, so in one hour it burns 1/6 of its total length. Therefore, after *t* number of hours, the portion of the candle that has burned is t/6, and the remaining length is (6 − t)/6. Similarly, the thinner candle has a total burning time of 4 hours, so it burns 1/4 of its length per hour. After *t* hours, the portion burned is t/4, and the remaining length is (4 − t)/4. To understand how values like 4/6 and 3/6 are obtained, we observe the thicker candle over time:| Hours | Thick Candle | Think Candle |
|---|---|---|
| 1 Hour | 5/6 | 3/4 |
| 2 Hours | 4/6 | 2/4 |
| 3 Hours | 3/6 | 1/4 |
