During Christmas, Will's candle and Perry's candle were placed on an altar. Will's candle was 20 cm longer than Perry's candle. Will's candle and Perry'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, Perry's candle was burnt out while Will's candle was burnt out at 1. Find the original height of each candle.
(a) Perry's candle
(b) Will's candle
| |
Will |
Perry |
Comparing the heights
of candles |
20 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 Will's candle burning → 2.5 hours of Perry's candle burning
10 hours of Will's candle burning → 5 hours of Perry's candle burning
Time taken for Perry's candle to burn 20 cm in height
= 5 - 1
= 4 h
4 hours of Perry's candle burning → 20 cm
1 hour of Perry's candle burning → 20 ÷ 4 = 5 cm
Total time taken for Perry's candle to burn
= 2.5 + 1
= 3.5 h
3.5 hours of Perry's candle burning
= 3.5 x 5
= 17.5 cm
Original height of Perry's candle = 17.5 cm
(b)
Original height of Will's candle
= 17.5 + 20
= 37.5 cm
Answer(s): (a) 17.5 cm; (b) 37.5 cm
