During Christmas, Will's candle and Glen's candle were placed on an altar. Will's candle was 4 cm longer than Glen's candle. Will's candle and Glen'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, Glen's candle was burnt out while Will's candle was burnt out at 1. Find the original height of each candle.
(a) Glen's candle
(b) Will's candle
| |
Will |
Glen |
Comparing the heights
of candles |
4 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 Will's candle burning → 2.5 hours of Glen's candle burning
10 hours of Will's candle burning → 5 hours of Glen's candle burning
Time taken for Glen's candle to burn 4 cm in height
= 5 - 3
= 2 h
2 hours of Glen's candle burning → 4 cm
1 hour of Glen's candle burning → 4 ÷ 2 = 2 cm
Total time taken for Glen's candle to burn
= 2.5 + 3
= 5.5 h
5.5 hours of Glen's candle burning
= 5.5 x 2
= 11 cm
Original height of Glen's candle = 11 cm
(b)
Original height of Will's candle
= 11 + 4
= 15 cm
Answer(s): (a) 11 cm; (b) 15 cm
