Two candles of the same height are lighted at the same time. The first...
We can let the height of both candles be 12 inches. So the first candle burns at a rate of 3 inches per hour and the second candle at a rate of 4 inches per hour. We can let x = the number of hours it takes the first candle to be twice the height of the second candle.
12 - 3x = 2(12 - 4x)
12 - 3x = 24 - 8x
5x = 12
x = 2.4 hours = 2 hours 24 minutes
View all questions of this test
Two candles of the same height are lighted at the same time. The first...
Understanding the Problem
To determine when the first candle will measure twice the height of the second, we first need to establish their burning rates and remaining heights over time.
Burning Rates of the Candles
- The first candle burns completely in 4 hours, meaning it burns at a rate of 1/4 of its height per hour.
- The second candle burns completely in 3 hours, so it burns at a rate of 1/3 of its height per hour.
Initial Heights of the Candles
Assuming both candles start at a height of 1 unit:
- After t hours, the height of the first candle:
Height1 = 1 - (1/4)t
- After t hours, the height of the second candle:
Height2 = 1 - (1/3)t
Setting Up the Equation
We want to find t when Height1 = 2 * Height2.
So, we set up the equation:
1 - (1/4)t = 2 * (1 - (1/3)t)
Simplifying the Equation
1 - (1/4)t = 2 - (2/3)t
To solve for t, rearranging gives us:
(2/3)t - (1/4)t = 1
Finding a common denominator (12):
(8/12)t - (3/12)t = 1
Combining terms:
(5/12)t = 1
Calculating t
t = 12/5 = 2.4 hours, which is equivalent to 2 hours and 24 minutes.
Conclusion
Thus, the first candle will measure twice the height of the second candle in 2 hours and 24 minutes, confirming that the correct answer is option B.