7. A store sells two kinds of candles, scented and unscented. The scented candles burn 1/12 inch in 20 min. The unscented candles burn 1/6 inch in 30 min. Which type of candle burns faster in 1 hour and what is its burn rate?
Answer: B
The scented candles burn faster, at a rate of 1/3 inch/hr.
To determine which type of candle burns faster, we need to calculate the burn rate for each type of candle over a standard time of one hour. The scented candles burn at a rate of 1/3 inch per hour, which is faster than the unscented candles.
A) The scented candles burn faster, at a rate of 1/4 inch/hr.
This option incorrectly states the burn rate of the scented candles. The calculation shows that they actually burn at a rate of 1/3 inch per hour, not 1/4 inch per hour, making this option inaccurate.
B) The scented candles burn faster, at a rate of 1/3 inch/hr.
This option correctly identifies that the scented candles burn faster. The calculation reveals that the scented candles burn 1/12 inch in 20 minutes, which translates to a burn rate of 1/3 inch per hour when scaled up to an hour.
C) The unscented candles burn faster, at a rate of 1/3 inch/hr.
This statement is incorrect as it claims the unscented candles burn faster. The unscented candles burn 1/6 inch in 30 minutes, which results in a burn rate of only 1/4 inch per hour, thus making them slower than the scented candles.
D) Both candles burn at the same rate of 1/4 inch/hr.
This option is incorrect as it asserts that both types of candles burn at the same rate. The calculations show that the scented candles burn at a rate of 1/3 inch per hour while the unscented candles burn at 1/4 inch per hour, indicating that they do not burn at the same rate.
Conclusion
The scented candles are definitively faster, burning at a rate of 1/3 inch per hour, while the unscented candles burn at a slower rate of 1/4 inch per hour. This comparison clearly demonstrates that option B is the correct answer, as it accurately reflects the burn rates calculated for both types of candles. All other options fail to provide correct information regarding the burn rates.