Candlestic!

Algebra Level 3

Chantelle had two candles, one of which was 3232 cm longer than the other. She lit the longer one at 33 p.m. and lit the shorter one at 77 p.m. At 99 p.m., they were both the same length. The longer one was completely burned out at 1010 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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