A blue candle is twice as long as a red candle. The blue candle takes 6 hours to burn out, and the red candle takes 15. After 5 hours, what fractional part of each candle is left? The blue candle's length is what fraction of the red candle's length? Explain how you got your answer.
well the blue candle's fraction left is 1/6 and the red candle's fraction is 1/3.
the blue candle's length is 1/2 of the red candle's existing length.
This is because after 5 hours there is only 1 hour left of the blue candle, and 10 hours left of the red candle giving you 1/6 left of the blue candle, and 1/3 (15/5=3)of the red candle left.
Since the blue candle 1/6 and the red candle 1/3: 1/6 is 1/2 of 1/3 therefor giving you the fraction 1/2 of the red candle is the existence of the blue candle.
To get the answer, we can break down the problem step by step:
1. First, let's calculate the fraction of each candle that is left after 5 hours:
- The blue candle burns out in 6 hours, so after 5 hours, there is 1 hour left. This means the fraction of the blue candle that is left is 1/6.
- The red candle burns out in 15 hours, so after 5 hours, there are 10 hours left. This means the fraction of the red candle that is left is 10/15, which simplifies to 2/3.
2. Now let's determine the fraction of the blue candle's length in comparison to the red candle's length:
- We know that the blue candle is twice as long as the red candle. Since the length of the blue candle is twice the length of the red candle, the ratio of their lengths is 2:1.
- To find the fraction, we need to compare the lengths of the blue and red candles. Let's assume the length of the red candle is 1 (you can use any unit of measurement here).
- Based on the ratio, the length of the blue candle would be 2 times the length of the red candle, which is 2/1 or simply 2.
Therefore, the fraction of the blue candle that is left after 5 hours is 1/6, the fraction of the red candle that is left after 5 hours is 2/3, and the blue candle's length is 1/2 of the red candle's length.