During Christmas, Eric's candle and Daniel's candle were placed on an altar. Eric's candle was 12 cm longer than Daniel's candle. Eric's candle and Daniel's candle were lit at 1.00 p.m. and 8.00 p.m. respectively. They burnt down to the same height at 11.00 p.m.. At 4, Daniel's candle was burnt out while Eric's candle was burnt out at 1. Find the original height of each candle.
(a) Daniel's candle
(b) Eric's candle
|
Eric |
Daniel |
Comparing the heights of candles |
12 cm more |
|
1 p.m. |
Lighted |
|
8 p.m. |
|
Lighted |
Burning time to reach same height |
10 h |
3 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 Eric's candle burning → 2.5 hours of Daniel's candle burning
10 hours of Eric's candle burning → 5 hours of Daniel's candle burning
Time taken for Daniel's candle to burn 12 cm in height
= 5 - 3
= 2 h
2 hours of Daniel's candle burning → 12 cm
1 hour of Daniel's candle burning → 12 ÷ 2 = 6 cm
Total time taken for Daniel's candle to burn
= 2.5 + 3
= 5.5 h
5.5 hours of Daniel's candle burning
= 5.5 x 6
= 33 cm
Original height of Daniel's candle = 33 cm
(b)
Original height of Eric's candle
= 33 + 12
= 45 cm
Answer(s): (a) 33 cm; (b) 45 cm