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