During Christmas, Harry's candle and Asher's candle were placed on an altar. Harry's candle was 8 cm longer than Asher's candle. Harry's candle and Asher's candle were lit at 1.00 p.m. and 10.00 p.m. respectively. They burnt down to the same height at 11.00 p.m.. At 4, Asher's candle was burnt out while Harry's candle was burnt out at 1. Find the original height of each candle.
(a) Asher's candle
(b) Harry's candle
| |
Harry |
Asher |
Comparing the heights
of candles |
8 cm more |
|
| 1 p.m. |
Lighted |
|
| 10 p.m. |
|
Lighted |
Burning time to
reach same height |
10 h |
1 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 Asher's candle burning
10 hours of Harry's candle burning → 5 hours of Asher's candle burning
Time taken for Asher's candle to burn 8 cm in height
= 5 - 1
= 4 h
4 hours of Asher's candle burning → 8 cm
1 hour of Asher's candle burning → 8 ÷ 4 = 2 cm
Total time taken for Asher's candle to burn
= 2.5 + 1
= 3.5 h
3.5 hours of Asher's candle burning
= 3.5 x 2
= 7 cm
Original height of Asher's candle = 7 cm
(b)
Original height of Harry's candle
= 7 + 8
= 15 cm
Answer(s): (a) 7 cm; (b) 15 cm
