During Christmas, Rael's candle and Flynn's candle were placed on an altar. Rael's candle was 12 cm longer than Flynn's candle. Rael's candle and Flynn'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, Flynn's candle was burnt out while Rael's candle was burnt out at 1. Find the original height of each candle.
(a) Flynn's candle
(b) Rael's candle
|
Rael |
Flynn |
Comparing the heights of candles |
12 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 Rael's candle burning → 2.5 hours of Flynn's candle burning
10 hours of Rael's candle burning → 5 hours of Flynn's candle burning
Time taken for Flynn's candle to burn 12 cm in height
= 5 - 1
= 4 h
4 hours of Flynn's candle burning → 12 cm
1 hour of Flynn's candle burning → 12 ÷ 4 = 3 cm
Total time taken for Flynn's candle to burn
= 2.5 + 1
= 3.5 h
3.5 hours of Flynn's candle burning
= 3.5 x 3
= 10.5 cm
Original height of Flynn's candle = 10.5 cm
(b)
Original height of Rael's candle
= 10.5 + 12
= 22.5 cm
Answer(s): (a) 10.5 cm; (b) 22.5 cm