# Candlestic!

Algebra Level 3

Chantelle had two candles, one of which was $$32$$ cm longer than the other. She lit the longer one at $$3$$ p.m. and lit the shorter one at $$7$$ p.m. At $$9$$ p.m., they were both the same length. The longer one was completely burned out at $$10$$ p.m. and the shorter one was completely burned at midnight. The two candles burned at different, but constant, rates. What was the sum of the original lengths of the two candles?

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