During Christmas, Howard's candle and Perry's candle were placed on an altar. Howard's candle was 12 cm longer than Perry's candle. Howard's candle and Perry's candle were lit at 1.00 p.m. and 8.00 p.m. respectively. They burnt down to the same height at 11.00 p.m.. At 4, Perry's candle was burnt out while Howard's candle was burnt out at 1. Find the original height of each candle.
(a) Perry's candle
(b) Howard's candle
|
Howard |
Perry |
Comparing the heights of candles |
12 cm more |
|
1 p.m. |
Lighted |
|
8 p.m. |
|
Lighted |
Burning time to reach same height |
10 h |
3 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 Perry's candle burning
10 hours of Howard's candle burning → 5 hours of Perry's candle burning
Time taken for Perry's candle to burn 12 cm in height
= 5 - 3
= 2 h
2 hours of Perry's candle burning → 12 cm
1 hour of Perry's candle burning → 12 ÷ 2 = 6 cm
Total time taken for Perry's candle to burn
= 2.5 + 3
= 5.5 h
5.5 hours of Perry's candle burning
= 5.5 x 6
= 33 cm
Original height of Perry's candle = 33 cm
(b)
Original height of Howard's candle
= 33 + 12
= 45 cm
Answer(s): (a) 33 cm; (b) 45 cm