During Christmas, Dylan's candle and Owen's candle were placed on an altar. Dylan's candle was 12 cm longer than Owen's candle. Dylan's candle and Owen'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, Owen's candle was burnt out while Dylan's candle was burnt out at 1. Find the original height of each candle.
(a) Owen's candle
(b) Dylan's candle
|
Dylan |
Owen |
Comparing the heights of candles |
12 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 Dylan's candle burning → 2.5 hours of Owen's candle burning
10 hours of Dylan's candle burning → 5 hours of Owen's candle burning
Time taken for Owen's candle to burn 12 cm in height
= 5 - 3
= 2 h
2 hours of Owen's candle burning → 12 cm
1 hour of Owen's candle burning → 12 ÷ 2 = 6 cm
Total time taken for Owen's candle to burn
= 2.5 + 3
= 5.5 h
5.5 hours of Owen's candle burning
= 5.5 x 6
= 33 cm
Original height of Owen's candle = 33 cm
(b)
Original height of Dylan's candle
= 33 + 12
= 45 cm
Answer(s): (a) 33 cm; (b) 45 cm