What was the sum of the original lengths of the two candles in centimeters?

Question

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 in centimeters?

Answer 1

Let initial length of the shorter candle be = x
Then the initial length of the longer candle = 32+x
length of both the candles are equal at 9:00
length of the longer candles at 9:00 = (32+x)*1/7 = length of the shorter candle at 9:00 = 3*(x/5)
or
3*(x/5) = (32+x)*1/7
x = 10 cm ( Original Length of the shorter candle )
32+x = 42 cm ( Original Length of the Longer candle )
Sum of the original lengths of the 2 candles = 10 + 42 = 52 cm.