During Christmas, Bryan's candle and Dylan's candle were placed on an altar. Bryan's candle was 6 cm longer than Dylan's candle. Bryan's candle and Dylan'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, Dylan's candle was burnt out while Bryan's candle was burnt out at 1. Find the original height of each candle.
(a) Dylan's candle
(b) Bryan's candle
|
Bryan |
Dylan |
Comparing the heights of candles |
6 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 Bryan's candle burning → 2.5 hours of Dylan's candle burning
10 hours of Bryan's candle burning → 5 hours of Dylan's candle burning
Time taken for Dylan's candle to burn 6 cm in height
= 5 - 2
= 3 h
3 hours of Dylan's candle burning → 6 cm
1 hour of Dylan's candle burning → 6 ÷ 3 = 2 cm
Total time taken for Dylan's candle to burn
= 2.5 + 2
= 4.5 h
4.5 hours of Dylan's candle burning
= 4.5 x 2
= 9 cm
Original height of Dylan's candle = 9 cm
(b)
Original height of Bryan's candle
= 9 + 6
= 15 cm
Answer(s): (a) 9 cm; (b) 15 cm