During Christmas, Elijah's candle and Carl's candle were placed on an altar. Elijah's candle was 20 cm longer than Carl's candle. Elijah's candle and Carl'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, Carl's candle was burnt out while Elijah's candle was burnt out at 1. Find the original height of each candle.
(a) Carl's candle
(b) Elijah's candle
| |
Elijah |
Carl |
Comparing the heights
of candles |
20 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 Elijah's candle burning → 2.5 hours of Carl's candle burning
10 hours of Elijah's candle burning → 5 hours of Carl's candle burning
Time taken for Carl's candle to burn 20 cm in height
= 5 - 1
= 4 h
4 hours of Carl's candle burning → 20 cm
1 hour of Carl's candle burning → 20 ÷ 4 = 5 cm
Total time taken for Carl's candle to burn
= 2.5 + 1
= 3.5 h
3.5 hours of Carl's candle burning
= 3.5 x 5
= 17.5 cm
Original height of Carl's candle = 17.5 cm
(b)
Original height of Elijah's candle
= 17.5 + 20
= 37.5 cm
Answer(s): (a) 17.5 cm; (b) 37.5 cm
