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