During Christmas, Luis's candle and George's candle were placed on an altar. Luis's candle was 18 cm longer than George's candle. Luis's candle and George'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, George's candle was burnt out while Luis's candle was burnt out at 1. Find the original height of each candle.
(a) George's candle
(b) Luis's candle
| |
Luis |
George |
Comparing the heights
of candles |
18 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 Luis's candle burning → 2.5 hours of George's candle burning
10 hours of Luis's candle burning → 5 hours of George's candle burning
Time taken for George's candle to burn 18 cm in height
= 5 - 2
= 3 h
3 hours of George's candle burning → 18 cm
1 hour of George's candle burning → 18 ÷ 3 = 6 cm
Total time taken for George's candle to burn
= 2.5 + 2
= 4.5 h
4.5 hours of George's candle burning
= 4.5 x 6
= 27 cm
Original height of George's candle = 27 cm
(b)
Original height of Luis's candle
= 27 + 18
= 45 cm
Answer(s): (a) 27 cm; (b) 45 cm
