During Christmas, Ethan's candle and Liam's candle were placed on an altar. Ethan's candle was 10 cm longer than Liam's candle. Ethan's candle and Liam'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, Liam's candle was burnt out while Ethan's candle was burnt out at 1. Find the original height of each candle.
(a) Liam's candle
(b) Ethan's candle
| |
Ethan |
Liam |
Comparing the heights
of candles |
10 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 Liam's candle burning
10 hours of Ethan's candle burning → 5 hours of Liam's candle burning
Time taken for Liam's candle to burn 10 cm in height
= 5 - 3
= 2 h
2 hours of Liam's candle burning → 10 cm
1 hour of Liam's candle burning → 10 ÷ 2 = 5 cm
Total time taken for Liam's candle to burn
= 2.5 + 3
= 5.5 h
5.5 hours of Liam's candle burning
= 5.5 x 5
= 27.5 cm
Original height of Liam's candle = 27.5 cm
(b)
Original height of Ethan's candle
= 27.5 + 10
= 37.5 cm
Answer(s): (a) 27.5 cm; (b) 37.5 cm
