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