Challenging P6

Candle A and candle B were placed on a table. Candle A was 1.5 cm longer than candle B. Candle A and candle B were lighted at 0630 h and 0800 h respectively. They burnt down to the same length at 1030 h. At 1200 h, candle B was burnt out while A only burnt out at 1230 h. Given that the rate of burning of each candle was constant throughout, find the original length of each candle.


            2 h              4 h
       | -------| ------------- |
 1230       1030                    0630
    [][][]  [][][]  [][][]
A [      ][       ][       ]        2 h -- 1 Bu; 4 h -- 2 Bu
B  [][][]  [][][]  [][]1.5cm     1.5 h -- 3 u; 2.5 h -- 5 u 
 1200      1030               0800  [1 Bu = 3 u, same length]
      |______|__________ |
        1.5 h           2.5 h

1 u --> 1.5 cm

A: 9 u --> 9 x 1.5 = 13.5 cm

B: 8 u --> 8 x 1.5 = 12 cm

The original lengths of candle A and candle B are 13.5 cm and 12 cm respectively.