During Christmas, Glen's candle and Seth's candle were placed on an altar. Glen's candle was 18 cm longer than Seth's candle. Glen's candle and Seth'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, Seth's candle was burnt out while Glen's candle was burnt out at 1. Find the original height of each candle.
(a) Seth's candle
(b) Glen's candle
|
Glen |
Seth |
Comparing the heights of candles |
18 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 Glen's candle burning → 2.5 hours of Seth's candle burning
10 hours of Glen's candle burning → 5 hours of Seth's candle burning
Time taken for Seth's candle to burn 18 cm in height
= 5 - 2
= 3 h
3 hours of Seth's candle burning → 18 cm
1 hour of Seth's candle burning → 18 ÷ 3 = 6 cm
Total time taken for Seth's candle to burn
= 2.5 + 2
= 4.5 h
4.5 hours of Seth's candle burning
= 4.5 x 6
= 27 cm
Original height of Seth's candle = 27 cm
(b)
Original height of Glen's candle
= 27 + 18
= 45 cm
Answer(s): (a) 27 cm; (b) 45 cm