During Christmas, Zane's candle and Harry's candle were placed on an altar. Zane's candle was 15 cm longer than Harry's candle. Zane's candle and Harry'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, Harry's candle was burnt out while Zane's candle was burnt out at 1. Find the original height of each candle.
(a) Harry's candle
(b) Zane's candle
|
Zane |
Harry |
Comparing the heights of candles |
15 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 Zane's candle burning → 2.5 hours of Harry's candle burning
10 hours of Zane's candle burning → 5 hours of Harry's candle burning
Time taken for Harry's candle to burn 15 cm in height
= 5 - 2
= 3 h
3 hours of Harry's candle burning → 15 cm
1 hour of Harry's candle burning → 15 ÷ 3 = 5 cm
Total time taken for Harry's candle to burn
= 2.5 + 2
= 4.5 h
4.5 hours of Harry's candle burning
= 4.5 x 5
= 22.5 cm
Original height of Harry's candle = 22.5 cm
(b)
Original height of Zane's candle
= 22.5 + 15
= 37.5 cm
Answer(s): (a) 22.5 cm; (b) 37.5 cm