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