Rates P6 2010 SA2 River Valley P2 Q17

Candle A and candle B are of the same length. Candle A, which is broader, can burn for 5 h while Candle B, the thinner candle, can burn for 4 h. If both candles are lighted at the same time, how long does it take for Candle A to be twice as long left as Candle B? [5 marks][Answer given: 3⅓ hours]

                       
A [        H            ] 5 h
B [        H            ] 4 h

AN [][] (5 - T) h
BN []  (4 - T) h

AN --> (5 - T)/5 H
BN --> (4 - T)/4 H

(5 - T)/5 H --> 2 x (4 - T)/4 H
2 x (5 - T) --> 5 x (4 - T)
10 - 2 T --> 20 - 5 T
3 T --> 20 - 10 = 10
T --> 10/3 = 3 1/3 h

It is 3 1/3 h.


Alternative method (model drawing)

Since Candle B burns faster, A - 4 units used up while B 5 units used up.
A [][][][][][] 5 h
B [][][][][][] 4 h

Using B,
5/6 x 4 = 10/3
            = 3 1/3 h

Or using A,
4/6 x 5 = 10/3
           = 3 1/3 h

It is 3 1/3 h.