During Christmas, Charlie's candle and Fabian's candle were placed on an altar. Charlie's candle was 20 cm longer than Fabian's candle. Charlie's candle and Fabian'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, Fabian's candle was burnt out while Charlie's candle was burnt out at 1. Find the original height of each candle.
(a) Fabian's candle
(b) Charlie's candle
| |
Charlie |
Fabian |
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 Charlie's candle burning → 2.5 hours of Fabian's candle burning
10 hours of Charlie's candle burning → 5 hours of Fabian's candle burning
Time taken for Fabian's candle to burn 20 cm in height
= 5 - 1
= 4 h
4 hours of Fabian's candle burning → 20 cm
1 hour of Fabian's candle burning → 20 ÷ 4 = 5 cm
Total time taken for Fabian's candle to burn
= 2.5 + 1
= 3.5 h
3.5 hours of Fabian's candle burning
= 3.5 x 5
= 17.5 cm
Original height of Fabian's candle = 17.5 cm
(b)
Original height of Charlie's candle
= 17.5 + 20
= 37.5 cm
Answer(s): (a) 17.5 cm; (b) 37.5 cm
