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