During Christmas, Peter's candle and Brandon's candle were placed on an altar. Peter's candle was 12 cm longer than Brandon's candle. Peter's candle and Brandon'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, Brandon's candle was burnt out while Peter's candle was burnt out at 1. Find the original height of each candle.
(a) Brandon's candle
(b) Peter's candle
|
Peter |
Brandon |
Comparing the heights of candles |
12 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 Peter's candle burning → 2.5 hours of Brandon's candle burning
10 hours of Peter's candle burning → 5 hours of Brandon's candle burning
Time taken for Brandon's candle to burn 12 cm in height
= 5 - 2
= 3 h
3 hours of Brandon's candle burning → 12 cm
1 hour of Brandon's candle burning → 12 ÷ 3 = 4 cm
Total time taken for Brandon's candle to burn
= 2.5 + 2
= 4.5 h
4.5 hours of Brandon's candle burning
= 4.5 x 4
= 18 cm
Original height of Brandon's candle = 18 cm
(b)
Original height of Peter's candle
= 18 + 12
= 30 cm
Answer(s): (a) 18 cm; (b) 30 cm