SOLUTION: Two different candles are lit. They burn at different rates and one is 3 cm longer than the other. The longer one was lit at 5:30 pm and the shorter one at 7 pm. At 9:30 pm they we

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Question 1146675: Two different candles are lit. They burn at different rates and one is 3 cm longer than the other. The longer one was lit at 5:30 pm and the shorter one at 7 pm. At 9:30 pm they were both the same length. The longer one burned out at 11:30 pm and the shorter one burned out at 11 pm. How long was each candle originally?
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Two different candles are lit.
They burn at different rates and one is 3 cm longer than the other.
The longer one was lit at 5:30 pm and the shorter one at 7 pm.
At 9:30 pm they were both the same length.
The longer one burned out at 11:30 pm and the shorter one burned out at 11 pm.
How long was each candle originally?
:
let a = the length of the longer candle
let b = the length of the shorter
:
the longer candle burned from 5:30 to 11:30 or 6 hrs, therefore
cm/hr is the rate of burn of the longer
and
the shorter candle burned from 7:00 to 11:00 or 4 hrs, therefore
cm/hr is the rate of burn for the shorter candle
:
at 9:30 the longer candle has burned for 4 hrs and the shorter for 2.5 hrs
a - 4* = b - 2.5*
a - = b -
multiply both sides by 12, get rid of the denominator
12a - 8a = 12b - 7.5b
4a = 4.5b
a is 3 cm longer than b, therefore
replace b with (a-3)
4a = 4.5(a-3)
4a = 4.5a - 13.5
4a - 4.5a = -13.5
-.5a = -13.5
a = -13.5/-.5
a = 27 cm is the longer candle
and obviously
24 cm is the shorter
:
see of this works out
27/6 = 4.5 cm/hr burn rate of the longer
24/4 = 6 cm/hr is the rate of the shorter
:
27 - 4(4.5) =
27 - 18 = 9 cm remain
and
24 - 2.5(6) =
24 - 15 = 9 cm remain