During Christmas, Perry's candle and Jack's candle were placed on an altar. Perry's candle was 6 cm longer than Jack's candle. Perry's candle and Jack'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, Jack's candle was burnt out while Perry's candle was burnt out at 1. Find the original height of each candle.
(a) Jack's candle
(b) Perry's candle
| |
Perry |
Jack |
Comparing the heights
of candles |
6 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 Perry's candle burning → 2.5 hours of Jack's candle burning
10 hours of Perry's candle burning → 5 hours of Jack's candle burning
Time taken for Jack's candle to burn 6 cm in height
= 5 - 2
= 3 h
3 hours of Jack's candle burning → 6 cm
1 hour of Jack's candle burning → 6 ÷ 3 = 2 cm
Total time taken for Jack's candle to burn
= 2.5 + 2
= 4.5 h
4.5 hours of Jack's candle burning
= 4.5 x 2
= 9 cm
Original height of Jack's candle = 9 cm
(b)
Original height of Perry's candle
= 9 + 6
= 15 cm
Answer(s): (a) 9 cm; (b) 15 cm
