During Christmas, Elijah's candle and Pierre's candle were placed on an altar. Elijah's candle was 10 cm longer than Pierre's candle. Elijah's candle and Pierre'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, Pierre's candle was burnt out while Elijah's candle was burnt out at 1. Find the original height of each candle.
(a) Pierre's candle
(b) Elijah's candle
| |
Elijah |
Pierre |
Comparing the heights
of candles |
10 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 Elijah's candle burning → 2.5 hours of Pierre's candle burning
10 hours of Elijah's candle burning → 5 hours of Pierre's candle burning
Time taken for Pierre's candle to burn 10 cm in height
= 5 - 3
= 2 h
2 hours of Pierre's candle burning → 10 cm
1 hour of Pierre's candle burning → 10 ÷ 2 = 5 cm
Total time taken for Pierre's candle to burn
= 2.5 + 3
= 5.5 h
5.5 hours of Pierre's candle burning
= 5.5 x 5
= 27.5 cm
Original height of Pierre's candle = 27.5 cm
(b)
Original height of Elijah's candle
= 27.5 + 10
= 37.5 cm
Answer(s): (a) 27.5 cm; (b) 37.5 cm
