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