During Christmas, Fabian's candle and Seth's candle were placed on an altar. Fabian's candle was 20 cm longer than Seth's candle. Fabian's candle and Seth's candle were lit at 1.00 p.m. and 10.00 p.m. respectively. They burnt down to the same height at 11.00 p.m.. At 4, Seth's candle was burnt out while Fabian's candle was burnt out at 1. Find the original height of each candle.
(a) Seth's candle
(b) Fabian's candle
| |
Fabian |
Seth |
Comparing the heights
of candles |
20 cm more |
|
| 1 p.m. |
Lighted |
|
| 10 p.m. |
|
Lighted |
Burning time to
reach same height |
10 h |
1 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 Fabian's candle burning → 2.5 hours of Seth's candle burning
10 hours of Fabian's candle burning → 5 hours of Seth's candle burning
Time taken for Seth's candle to burn 20 cm in height
= 5 - 1
= 4 h
4 hours of Seth's candle burning → 20 cm
1 hour of Seth's candle burning → 20 ÷ 4 = 5 cm
Total time taken for Seth's candle to burn
= 2.5 + 1
= 3.5 h
3.5 hours of Seth's candle burning
= 3.5 x 5
= 17.5 cm
Original height of Seth's candle = 17.5 cm
(b)
Original height of Fabian's candle
= 17.5 + 20
= 37.5 cm
Answer(s): (a) 17.5 cm; (b) 37.5 cm
