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Burning Down

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Let the height of the shorter candle be x and the height of the taller candle be x + 3. Assume that the short candle burns down at a cm per hour and the tall candle burns down at b cm per hour.

The candles are the same length at 9.30 so:

x - 2.5a = x +3 - 4b (1)

Also the short candle burns out after 4 hours so:

4a = x (2)

and the tall candle burns out after 6 hours so:

6b= x +3 (3)

Using equations 1,2 and 3 gives rise to

x - 2.5x /4 =x +3 - 4(x+3)/6

which when solved gives x = 24cm

Finally, originally the shorter candle was 24cm and the longer one was 27cm.