SOLUTION: I don't know where to begin with this problem!! Please help. Thanks you. A candle is lit at 5:30 p.m. Another candle, 1 cm shorter than the first, is lit at 7 p.m. The can

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Question 87074: I don't know where to begin with this problem!! Please help. Thanks you.
A candle is lit at 5:30 p.m. Another candle, 1 cm shorter than the first, is lit at 7 p.m. The candles are the same length at 9:30 p.m. The first candle burns out at 11:30 p.m. and the second one at 11:00 p.m. How tall was the longer candle?
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Each candle has a rate of burn, and what is being assumed in
the problem (and of course is debateable) is that the rate of
burn for each is constant and may be different for each candle.
The rate of burn is how far it burns down in a given time period.
First look at when each is lit and when it burns out.
Call the 1st one candle A and the 2nd one candle B.
The rate of burn for A is
The rate of burn for B is
Call the starting height of A in cm
The is the starting height of B in cm
From 5:30 to 11:30 for A is 6 hours
From 7:00 to 11:00 for B is 4 hours

Now look at the information relating to the candles being the same
height at 9:30. Candle A will burn down the same amount as B plus an
extra cm.
So, in words, (A's rate)(A's time) = (B's rate)(B's time) + 1 cm
A's time is 4 hrs, and B's time is 2.5 hours

multiple both sides by LCD which is 12

multiply both sides by 2

So, the height of the longest candle is 9 cm
Check this by plugging back into equations
What are the rates of A and B?

How about the rate*time for each to burn all the way down?

h = 9

OK