Estimating Time and Cost with Candles: A Mathematical Puzzle

The question posed, 'A large candle burns for 1 hour and costs 60 cents. A small candle burns for 11 minutes and costs 11 cents. Is it possible to estimate the time of 1 minute at a price of 150 cents?' is a classic puzzle in mathematics, often assigned in third-grade classrooms to challenge young minds. This article will delve into the details of this puzzle, providing a clear and logical explanation.

Understanding the Basic Information

Let's begin by unpacking the information given:

Large Candle: Burns for 1 hour (60 minutes) and costs 60 cents. Small Candle: Burns for 11 minutes and costs 11 cents.

The fundamental question here is whether the 150 cents can be used to estimate the time of 1 minute.

Calculating the Cost per Minute for Both Candles

To tackle this problem, we need to calculate the cost per minute for both large and small candles:

Large Candle:

Cost per minute 60 cents / 60 minutes 1 cent per minute.

Small Candle:

Cost per minute 11 cents / 11 minutes 1 cent per minute.

Interestingly, both candles have an average burn rate of 1 cent per minute. This is the key insight needed to solve the puzzle.

Tackling the Puzzle: Estimating the Burn Time

Given that both candles burn at an average rate of 1 cent per minute, we can extend this logic to a 150 cents candle. If the average cost per minute is 1 cent, then:

150 cents / 1 cent per minute 150 minutes.

This means that a 150 cents candle would burn for 150 minutes, assuming the same average burn rate.

Additional Considerations and Theoretical Insights

It is important to note that while the average burn rate of both candles is 1 cent per minute, there is no definitive proof that a 150 cents candle will burn for exactly the same duration at 1 cent per minute rate. Different burn rates over time could lead to variations in the actual burn time. However, the problem assumes the candles burn on average at that rate, making the 150 cents equivalent to 150 minutes.

Conclusion

In summary, based on the given information and the average burn rate of the candles, a 150 cents candle would theoretically burn for 150 minutes. This conclusion is drawn assuming the candles maintain an average burn rate of 1 cent per minute. If you are looking for practical applications or real-world interpretations, the puzzle serves as a fun and engaging exercise in mathematical reasoning.

Whether you are a teacher, a student, or just someone who enjoys mathematical puzzles, understanding these principles can be a valuable learning experience.