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