During Christmas, Ethan's candle and Will's candle were placed on an altar. Ethan's candle was 6 cm longer than Will's candle. Ethan's candle and Will's candle were lit at 1.00 p.m. and 8.00 p.m. respectively. They burnt down to the same height at 11.00 p.m.. At 4, Will's candle was burnt out while Ethan's candle was burnt out at 1. Find the original height of each candle.
(a) Will's candle
(b) Ethan's candle
| |
Ethan |
Will |
Comparing the heights
of candles |
6 cm more |
|
| 1 p.m. |
Lighted |
|
| 8 p.m. |
|
Lighted |
Burning time to
reach same height |
10 h |
3 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 Ethan's candle burning → 2.5 hours of Will's candle burning
10 hours of Ethan's candle burning → 5 hours of Will's candle burning
Time taken for Will's candle to burn 6 cm in height
= 5 - 3
= 2 h
2 hours of Will's candle burning → 6 cm
1 hour of Will's candle burning → 6 ÷ 2 = 3 cm
Total time taken for Will's candle to burn
= 2.5 + 3
= 5.5 h
5.5 hours of Will's candle burning
= 5.5 x 3
= 16.5 cm
Original height of Will's candle = 16.5 cm
(b)
Original height of Ethan's candle
= 16.5 + 6
= 22.5 cm
Answer(s): (a) 16.5 cm; (b) 22.5 cm
