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Two candles of the same height are lighted at the same time. The first is consumed in 4 hours and the second in 3 hours. Assuming that each candle burns at a constant rate, in how many hours after being lighted was the first candle twice the height of the second?
- a)3/4 hour
- b)11/2 hour
- c)4 hour
- d)12/5 hour
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Answer:
Let's assume the height of both candles is 'h' units.
Step 1:
In 4 hours, the first candle is consumed, so its height becomes 0 units.
In the same 4 hours, the second candle is consumed to a height of h/3 units.
Step 2:
Now, let's assume that after 't' hours, the height of the first candle is twice the height of the second candle.
So, the height of the first candle after 't' hours is 2 * (h/3) = 2h/3 units.
Step 3:
We know that the first candle burns at a constant rate, so its height decreases linearly with time.
The rate of decrease in height of the first candle is h/4 units per hour.
Step 4:
We can set up the equation for the height of the first candle after 't' hours:
h - (h/4) * t = 2h/3
Step 5:
Simplifying the equation:
h(1 - 1/4t) = 2h/3
(1 - 1/4t) = 2/3
1 - 1/4t = 2/3
1/4t = 1/3
t = 4/3 * 4 = 16/3 = 5 1/3
Therefore, the first candle was twice the height of the second candle after 16/3 hours or 5 1/3 hours.
Hence, the correct answer is option D) 12/5 hour.
Let's assume the height of both candles is 'h' units.
Step 1:
In 4 hours, the first candle is consumed, so its height becomes 0 units.
In the same 4 hours, the second candle is consumed to a height of h/3 units.
Step 2:
Now, let's assume that after 't' hours, the height of the first candle is twice the height of the second candle.
So, the height of the first candle after 't' hours is 2 * (h/3) = 2h/3 units.
Step 3:
We know that the first candle burns at a constant rate, so its height decreases linearly with time.
The rate of decrease in height of the first candle is h/4 units per hour.
Step 4:
We can set up the equation for the height of the first candle after 't' hours:
h - (h/4) * t = 2h/3
Step 5:
Simplifying the equation:
h(1 - 1/4t) = 2h/3
(1 - 1/4t) = 2/3
1 - 1/4t = 2/3
1/4t = 1/3
t = 4/3 * 4 = 16/3 = 5 1/3
Therefore, the first candle was twice the height of the second candle after 16/3 hours or 5 1/3 hours.
Hence, the correct answer is option D) 12/5 hour.
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