During Christmas, Pierre's candle and Elijah's candle were placed on an altar. Pierre's candle was 4 cm longer than Elijah's candle. Pierre's candle and Elijah's candle were lit at 1.00 p.m. and 8.00 p.m. respectively. They burnt down to the same height at 11.00 p.m.. At 4, Elijah's candle was burnt out while Pierre's candle was burnt out at 1. Find the original height of each candle.
(a) Elijah's candle
(b) Pierre's candle
|
Pierre |
Elijah |
Comparing the heights of candles |
4 cm more |
|
1 p.m. |
Lighted |
|
8 p.m. |
|
Lighted |
Burning time to reach same height |
10 h |
3 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 Pierre's candle burning → 2.5 hours of Elijah's candle burning
10 hours of Pierre's candle burning → 5 hours of Elijah's candle burning
Time taken for Elijah's candle to burn 4 cm in height
= 5 - 3
= 2 h
2 hours of Elijah's candle burning → 4 cm
1 hour of Elijah's candle burning → 4 ÷ 2 = 2 cm
Total time taken for Elijah's candle to burn
= 2.5 + 3
= 5.5 h
5.5 hours of Elijah's candle burning
= 5.5 x 2
= 11 cm
Original height of Elijah's candle = 11 cm
(b)
Original height of Pierre's candle
= 11 + 4
= 15 cm
Answer(s): (a) 11 cm; (b) 15 cm