Brainteaser #26- Candlelight Dinner -
A man lights two candles and begins a romantic candlelight dinner with his wife. The candles are of
equal length, but one candle is thicker than the other. The thick candle is designed to last for six
hours while the thin candle is designed to last for three hours.
At the end of the dinner, the thick candle is twice as long as the thin candle. How long did their
dinner last?
HINT: One way of tackling the problem is by assigning a hypothetical length to the
initial length of the candles, for example 6 inches, and then solving by trial and error.
ANSWER:
2 hours.
EXPLANATION: Let
L represent the initial length of the candles and
H the number of hours the candles have been lit. The length of the candles at the end of
the dinner can be written as
L - (H/6 × L) for the thick candle and
L - (H/3
× L) for the thin candle. At the end of the dinner, the thick candle is twice is long as
the thin candle, so:
- L - (H/6 × L) = 2 × (L - (H/3 × L))
- L - HL/6 = 2L - 2HL/3
- L - HL/6 = 2L - 4HL/6
- 4HL/6 - HL/6 = L
- 3HL/6 = L
- 3HL = 6L
- H = 2 hours
Do you have a
suggestion for this puzzle (e.g. something that should
be mentioned/clarified in the question or solution, bug, typo, etc.)?
