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