During Christmas, Nick's candle and Henry's candle were placed on an altar. Nick's candle was 12 cm longer than Henry's candle. Nick's candle and Henry'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, Henry's candle was burnt out while Nick's candle was burnt out at 1. Find the original height of each candle.
(a) Henry's candle
(b) Nick's candle
|
Nick |
Henry |
Comparing the heights of candles |
12 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 Nick's candle burning → 2.5 hours of Henry's candle burning
10 hours of Nick's candle burning → 5 hours of Henry's candle burning
Time taken for Henry's candle to burn 12 cm in height
= 5 - 1
= 4 h
4 hours of Henry's candle burning → 12 cm
1 hour of Henry's candle burning → 12 ÷ 4 = 3 cm
Total time taken for Henry's candle to burn
= 2.5 + 1
= 3.5 h
3.5 hours of Henry's candle burning
= 3.5 x 3
= 10.5 cm
Original height of Henry's candle = 10.5 cm
(b)
Original height of Nick's candle
= 10.5 + 12
= 22.5 cm
Answer(s): (a) 10.5 cm; (b) 22.5 cm