During Christmas, Tommy's candle and Ken's candle were placed on an altar. Tommy's candle was 10 cm longer than Ken's candle. Tommy's candle and Ken'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, Ken's candle was burnt out while Tommy's candle was burnt out at 1. Find the original height of each candle.
(a) Ken's candle
(b) Tommy's candle
| |
Tommy |
Ken |
Comparing the heights
of candles |
10 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 Tommy's candle burning → 2.5 hours of Ken's candle burning
10 hours of Tommy's candle burning → 5 hours of Ken's candle burning
Time taken for Ken's candle to burn 10 cm in height
= 5 - 3
= 2 h
2 hours of Ken's candle burning → 10 cm
1 hour of Ken's candle burning → 10 ÷ 2 = 5 cm
Total time taken for Ken's candle to burn
= 2.5 + 3
= 5.5 h
5.5 hours of Ken's candle burning
= 5.5 x 5
= 27.5 cm
Original height of Ken's candle = 27.5 cm
(b)
Original height of Tommy's candle
= 27.5 + 10
= 37.5 cm
Answer(s): (a) 27.5 cm; (b) 37.5 cm
