During Christmas, Julian's candle and Andy's candle were placed on an altar. Julian's candle was 24 cm longer than Andy's candle. Julian's candle and Andy'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, Andy's candle was burnt out while Julian's candle was burnt out at 1. Find the original height of each candle.
(a) Andy's candle
(b) Julian's candle
|
Julian |
Andy |
Comparing the heights of candles |
24 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 Julian's candle burning → 2.5 hours of Andy's candle burning
10 hours of Julian's candle burning → 5 hours of Andy's candle burning
Time taken for Andy's candle to burn 24 cm in height
= 5 - 1
= 4 h
4 hours of Andy's candle burning → 24 cm
1 hour of Andy's candle burning → 24 ÷ 4 = 6 cm
Total time taken for Andy's candle to burn
= 2.5 + 1
= 3.5 h
3.5 hours of Andy's candle burning
= 3.5 x 6
= 21 cm
Original height of Andy's candle = 21 cm
(b)
Original height of Julian's candle
= 21 + 24
= 45 cm
Answer(s): (a) 21 cm; (b) 45 cm