SOLUTION: two candles of the same height are lit at the same time. each candle burns at a constant rate and the first candle takes 5 hours while the second candle takes 4 hours to burn compl

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Question 477023: two candles of the same height are lit at the same time. each candle burns at a constant rate and the first candle takes 5 hours while the second candle takes 4 hours to burn completely. find the time, in hours, taken for the height of the first candle to be four time that of the second candle
Answer by josmiceli(9680) About Me  (Show Source):
You can put this solution on YOUR website!
Let +h%5B0%5D+ = the height that both candles start at
Let +h%5B1%5D+ = the current height of the 1st candle
Let +h%5B2%5D+ = the current height of the 2nd candle
Let +t+ = the current time expired in hours
given:
+h%5B0%5D+%2F+5+ = the rate of burning of the 1st candle
+h%5B0%5D+%2F+4+ = the rate of burning of the 2nd candle
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For the 1st candle:
(1) +h%5B1%5D+=+h%5B0%5D+-+%28+h%5B0%5D%2F5+%29%2At+
For the 2nd candle:
(2) +h%5B2%5D+=+h%5B0%5D+-+%28+h%5B0%5D%2F4+%29%2At+
--------------
given:
+h%5B1%5D+=+4h%5B2%5D+
(1) +4h%5B2%5D+=+h%5B0%5D%2A%281+-+t%2F5%29+
(1) +h%5B2%5D+=+%28+h%5B0%5D%2A%281+-+t%2F5%29%29%2F4+
and
(2) +h%5B2%5D+=+h%5B0%5D%2A%281+-+t%2F4%29+
------------------------
I can set the right sides equal to each other
+%28+h%5B0%5D%2A%281+-+t%2F5%29%29%2F4+=+h%5B0%5D%2A%281+-+t%2F4%29+
Divide both sides by +h%5B0%5D+
++%281+-+t%2F5%29%2F4+=+1+-+t%2F4+
Multiply both sides by 4
+1+-+t%2F5+=+4+-+t+
Multiply both sides by 5
+5+-+t+=+20+-+5t+
+4t+=+20+-+5+
+4t+=+15+
+t+=+3.75+
It will take 3 hrs and 45 min for the
1st candle to be 4 times as high as the 2nd candle
check answer:
Suppose the heights of both start at 1 m
For the 1st candle:
For the 1st candle:
(1) +h%5B1%5D+=+1+-+%28+1%2F5+%29%2A3.75+
(1) +h%5B1%5D+=+1+-+.2%2A3.75+
(1) +h%5B1%5D+=+1+-+.75+
(1) +h%5B1%5D+=+.25+
For the 2nd candle:
(2) +h%5B2%5D+=+1+-+%28+1%2F4+%29%2A3.75+
(2) +h%5B2%5D+=+1+-+.25%2A3.75+
(2) +h%5B2%5D+=+1+-+.9375+
(2) +h%5B2%5D+=+.0625+
and
+h%5B1%5D+%2F+h%5B2%5D+=+.25%2F.0625+
+h%5B1%5D+%2F+h%5B2%5D+=+4+
OK