AlgebraVery hardWhen one candle is twice the length of another
Algebra practice question
Two candles are the same length. One burns out completely in 4 hours and the other in 6 hours, each at a steady rate. After how many hours of burning will the slower candle be exactly twice as long as the faster one?
Answer: 3
After t hours the fractions remaining are 1 − t/4 and 1 − t/6. Setting 1 − t/6 = 2(1 − t/4) gives t/2 − t/6 = 1, so t = 3.
Common wrong answers
- If you answered 2
- 2 gives remaining fractions 1/2 and 2/3, not a 2 : 1 ratio.
- If you answered 4
- 4 is when the faster candle is gone entirely.
- If you answered 1.5
- 1.5 comes from t/3 = 1/2, a slip in combining the fractions.
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