During Christmas, Jeremy's candle and Gabriel's candle were placed on an altar. Jeremy's candle was 15 cm longer than Gabriel's candle. Jeremy's candle and Gabriel'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, Gabriel's candle was burnt out while Jeremy's candle was burnt out at 1. Find the original height of each candle.
(a) Gabriel's candle
(b) Jeremy's candle
| |
Jeremy |
Gabriel |
Comparing the heights
of candles |
15 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 Gabriel's candle burning
10 hours of Jeremy's candle burning → 5 hours of Gabriel's candle burning
Time taken for Gabriel's candle to burn 15 cm in height
= 5 - 2
= 3 h
3 hours of Gabriel's candle burning → 15 cm
1 hour of Gabriel's candle burning → 15 ÷ 3 = 5 cm
Total time taken for Gabriel's candle to burn
= 2.5 + 2
= 4.5 h
4.5 hours of Gabriel's candle burning
= 4.5 x 5
= 22.5 cm
Original height of Gabriel's candle = 22.5 cm
(b)
Original height of Jeremy's candle
= 22.5 + 15
= 37.5 cm
Answer(s): (a) 22.5 cm; (b) 37.5 cm
