During Christmas, Daniel's candle and Luis's candle were placed on an altar. Daniel's candle was 9 cm longer than Luis's candle. Daniel's candle and Luis'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, Luis's candle was burnt out while Daniel's candle was burnt out at 1. Find the original height of each candle.
(a) Luis's candle
(b) Daniel's candle
| |
Daniel |
Luis |
Comparing the heights
of candles |
9 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 Daniel's candle burning → 2.5 hours of Luis's candle burning
10 hours of Daniel's candle burning → 5 hours of Luis's candle burning
Time taken for Luis's candle to burn 9 cm in height
= 5 - 2
= 3 h
3 hours of Luis's candle burning → 9 cm
1 hour of Luis's candle burning → 9 ÷ 3 = 3 cm
Total time taken for Luis's candle to burn
= 2.5 + 2
= 4.5 h
4.5 hours of Luis's candle burning
= 4.5 x 3
= 13.5 cm
Original height of Luis's candle = 13.5 cm
(b)
Original height of Daniel's candle
= 13.5 + 9
= 22.5 cm
Answer(s): (a) 13.5 cm; (b) 22.5 cm
