During Christmas, Jeremy's candle and Jenson's candle were placed on an altar. Jeremy's candle was 9 cm longer than Jenson's candle. Jeremy's candle and Jenson'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, Jenson's candle was burnt out while Jeremy's candle was burnt out at 1. Find the original height of each candle.
(a) Jenson's candle
(b) Jeremy's candle
|
Jeremy |
Jenson |
Comparing the heights of candles |
9 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 Jeremy's candle burning → 2.5 hours of Jenson's candle burning
10 hours of Jeremy's candle burning → 5 hours of Jenson's candle burning
Time taken for Jenson's candle to burn 9 cm in height
= 5 - 2
= 3 h
3 hours of Jenson's candle burning → 9 cm
1 hour of Jenson's candle burning → 9 ÷ 3 = 3 cm
Total time taken for Jenson's candle to burn
= 2.5 + 2
= 4.5 h
4.5 hours of Jenson's candle burning
= 4.5 x 3
= 13.5 cm
Original height of Jenson's candle = 13.5 cm
(b)
Original height of Jeremy's candle
= 13.5 + 9
= 22.5 cm
Answer(s): (a) 13.5 cm; (b) 22.5 cm