During Christmas, Jenson's candle and Ahmad's candle were placed on an altar. Jenson's candle was 12 cm longer than Ahmad's candle. Jenson's candle and Ahmad's candle were lit at 1.00 p.m. and 9.00 p.m. respectively. They burnt down to the same height at 11.00 p.m.. At 4, Ahmad's candle was burnt out while Jenson's candle was burnt out at 1. Find the original height of each candle.
(a) Ahmad's candle
(b) Jenson's candle
| |
Jenson |
Ahmad |
Comparing the heights
of candles |
12 cm more |
|
| 1 p.m. |
Lighted |
|
| 9 p.m. |
|
Lighted |
Burning time to
reach same height |
10 h |
2 h |
| 11 p.m. |
Same height |
| 4 a.m. |
|
Burnt out |
| 1.30 a.m. |
Burnt out |
|
Remaining burning time
for each candle to burn out |
5 h |
2.5 h |
(a)
After reaching the same height, total remaining burning time for each candle to burn out:
5 hours of Jenson's candle burning → 2.5 hours of Ahmad's candle burning
10 hours of Jenson's candle burning → 5 hours of Ahmad's candle burning
Time taken for Ahmad's candle to burn 12 cm in height
= 5 - 2
= 3 h
3 hours of Ahmad's candle burning → 12 cm
1 hour of Ahmad's candle burning → 12 ÷ 3 = 4 cm
Total time taken for Ahmad's candle to burn
= 2.5 + 2
= 4.5 h
4.5 hours of Ahmad's candle burning
= 4.5 x 4
= 18 cm
Original height of Ahmad's candle = 18 cm
(b)
Original height of Jenson's candle
= 18 + 12
= 30 cm
Answer(s): (a) 18 cm; (b) 30 cm
