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One candle was guaranteed to burn for 6 hours, the other for 2 hours. They were both lit at same time. After some time one candle was twice as long as the other. For how long had they been burning?
- a)3 hours
- b)6 hours
- c)4/3 hours
- d)3/2 hours
Correct answer is option 'C'. Can you explain this answer?
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One candle was guaranteed to burn for 6 hours, the other for 2 hours. ...
Let the candles have burnt for ‘x’ hours,
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Most Upvoted Answer
One candle was guaranteed to burn for 6 hours, the other for 2 hours. ...
Given information:
- One candle burns for 6 hours.
- Another candle burns for 2 hours.
- Both candles were lit at the same time.
- After some time, one candle is twice as long as the other.
To find:
The time for which the candles have been burning.
Explanation:
Let's assume that the slower-burning candle is shorter and the faster-burning candle is longer. Initially, both candles have the same length.
After some time, the slower-burning candle will burn out completely, while the faster-burning candle will still have some length left.
Let's assume that the slower-burning candle burns out after t hours and the faster-burning candle is twice as long as the slower-burning candle after t hours.
Calculating the lengths of the candles:
- The slower-burning candle burns at a rate of 1/6 of its length per hour. So, after t hours, its length will be (1 - t/6) times its original length.
- The faster-burning candle burns at a rate of 1/2 of its length per hour. So, after t hours, its length will be (1 - t/2) times its original length.
Setting up the equation:
From the given information, we know that the length of the faster-burning candle is twice the length of the slower-burning candle after t hours.
(1 - t/2) times the original length of the faster-burning candle = 2 * (1 - t/6) times the original length of the slower-burning candle
Simplifying the equation:
1 - t/2 = 2 - t/3
t/2 - t/3 = 1
(3t - 2t)/6 = 1
t/6 = 1
t = 6
Conclusion:
The candles have been burning for 6 hours.
Therefore, the correct answer is option C) 4/3 hours.
- One candle burns for 6 hours.
- Another candle burns for 2 hours.
- Both candles were lit at the same time.
- After some time, one candle is twice as long as the other.
To find:
The time for which the candles have been burning.
Explanation:
Let's assume that the slower-burning candle is shorter and the faster-burning candle is longer. Initially, both candles have the same length.
After some time, the slower-burning candle will burn out completely, while the faster-burning candle will still have some length left.
Let's assume that the slower-burning candle burns out after t hours and the faster-burning candle is twice as long as the slower-burning candle after t hours.
Calculating the lengths of the candles:
- The slower-burning candle burns at a rate of 1/6 of its length per hour. So, after t hours, its length will be (1 - t/6) times its original length.
- The faster-burning candle burns at a rate of 1/2 of its length per hour. So, after t hours, its length will be (1 - t/2) times its original length.
Setting up the equation:
From the given information, we know that the length of the faster-burning candle is twice the length of the slower-burning candle after t hours.
(1 - t/2) times the original length of the faster-burning candle = 2 * (1 - t/6) times the original length of the slower-burning candle
Simplifying the equation:
1 - t/2 = 2 - t/3
t/2 - t/3 = 1
(3t - 2t)/6 = 1
t/6 = 1
t = 6
Conclusion:
The candles have been burning for 6 hours.
Therefore, the correct answer is option C) 4/3 hours.
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One candle was guaranteed to burn for 6 hours, the other for 2 hours. They were both lit at same time. After some time one candle was twice as long as the other. For how long had they been burning?a)3 hoursb)6 hoursc)4/3hoursd)3/2hoursCorrect answer is option 'C'. Can you explain this answer?
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