During Christmas, Simon's candle and Rael's candle were placed on an altar. Simon's candle was 8 cm longer than Rael's candle. Simon's candle and Rael'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, Rael's candle was burnt out while Simon's candle was burnt out at 1. Find the original height of each candle.
(a) Rael's candle
(b) Simon's candle
|
Simon |
Rael |
Comparing the heights of candles |
8 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 Rael's candle burning
10 hours of Simon's candle burning → 5 hours of Rael's candle burning
Time taken for Rael's candle to burn 8 cm in height
= 5 - 1
= 4 h
4 hours of Rael's candle burning → 8 cm
1 hour of Rael's candle burning → 8 ÷ 4 = 2 cm
Total time taken for Rael's candle to burn
= 2.5 + 1
= 3.5 h
3.5 hours of Rael's candle burning
= 3.5 x 2
= 7 cm
Original height of Rael's candle = 7 cm
(b)
Original height of Simon's candle
= 7 + 8
= 15 cm
Answer(s): (a) 7 cm; (b) 15 cm