During Christmas, Asher's candle and Dylan's candle were placed on an altar. Asher's candle was 12 cm longer than Dylan's candle. Asher's candle and Dylan'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, Dylan's candle was burnt out while Asher's candle was burnt out at 1. Find the original height of each candle.
(a) Dylan's candle
(b) Asher's candle
| |
Asher |
Dylan |
Comparing the heights
of candles |
12 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 Asher's candle burning → 2.5 hours of Dylan's candle burning
10 hours of Asher's candle burning → 5 hours of Dylan's candle burning
Time taken for Dylan's candle to burn 12 cm in height
= 5 - 1
= 4 h
4 hours of Dylan's candle burning → 12 cm
1 hour of Dylan's candle burning → 12 ÷ 4 = 3 cm
Total time taken for Dylan's candle to burn
= 2.5 + 1
= 3.5 h
3.5 hours of Dylan's candle burning
= 3.5 x 3
= 10.5 cm
Original height of Dylan's candle = 10.5 cm
(b)
Original height of Asher's candle
= 10.5 + 12
= 22.5 cm
Answer(s): (a) 10.5 cm; (b) 22.5 cm
