During Christmas, Luke's candle and Vincent's candle were placed on an altar. Luke's candle was 12 cm longer than Vincent's candle. Luke's candle and Vincent'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, Vincent's candle was burnt out while Luke's candle was burnt out at 1. Find the original height of each candle.
(a) Vincent's candle
(b) Luke's candle
|
Luke |
Vincent |
Comparing the heights of candles |
12 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 Luke's candle burning → 2.5 hours of Vincent's candle burning
10 hours of Luke's candle burning → 5 hours of Vincent's candle burning
Time taken for Vincent's candle to burn 12 cm in height
= 5 - 2
= 3 h
3 hours of Vincent's candle burning → 12 cm
1 hour of Vincent's candle burning → 12 ÷ 3 = 4 cm
Total time taken for Vincent's candle to burn
= 2.5 + 2
= 4.5 h
4.5 hours of Vincent's candle burning
= 4.5 x 4
= 18 cm
Original height of Vincent's candle = 18 cm
(b)
Original height of Luke's candle
= 18 + 12
= 30 cm
Answer(s): (a) 18 cm; (b) 30 cm