During Christmas, Simon's candle and Vaidev's candle were placed on an altar. Simon's candle was 20 cm longer than Vaidev's candle. Simon's candle and Vaidev'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, Vaidev's candle was burnt out while Simon's candle was burnt out at 1. Find the original height of each candle.
(a) Vaidev's candle
(b) Simon's candle
| |
Simon |
Vaidev |
Comparing the heights
of candles |
20 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 Simon's candle burning → 2.5 hours of Vaidev's candle burning
10 hours of Simon's candle burning → 5 hours of Vaidev's candle burning
Time taken for Vaidev's candle to burn 20 cm in height
= 5 - 1
= 4 h
4 hours of Vaidev's candle burning → 20 cm
1 hour of Vaidev's candle burning → 20 ÷ 4 = 5 cm
Total time taken for Vaidev's candle to burn
= 2.5 + 1
= 3.5 h
3.5 hours of Vaidev's candle burning
= 3.5 x 5
= 17.5 cm
Original height of Vaidev's candle = 17.5 cm
(b)
Original height of Simon's candle
= 17.5 + 20
= 37.5 cm
Answer(s): (a) 17.5 cm; (b) 37.5 cm
