During Christmas, Simon's candle and Zeph's candle were placed on an altar. Simon's candle was 18 cm longer than Zeph's candle. Simon's candle and Zeph'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, Zeph's candle was burnt out while Simon's candle was burnt out at 1. Find the original height of each candle.
(a) Zeph's candle
(b) Simon's candle
|
Simon |
Zeph |
Comparing the heights of candles |
18 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 Simon's candle burning → 2.5 hours of Zeph's candle burning
10 hours of Simon's candle burning → 5 hours of Zeph's candle burning
Time taken for Zeph's candle to burn 18 cm in height
= 5 - 2
= 3 h
3 hours of Zeph's candle burning → 18 cm
1 hour of Zeph's candle burning → 18 ÷ 3 = 6 cm
Total time taken for Zeph's candle to burn
= 2.5 + 2
= 4.5 h
4.5 hours of Zeph's candle burning
= 4.5 x 6
= 27 cm
Original height of Zeph's candle = 27 cm
(b)
Original height of Simon's candle
= 27 + 18
= 45 cm
Answer(s): (a) 27 cm; (b) 45 cm