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