During Christmas, Tom's candle and Ian's candle were placed on an altar. Tom's candle was 15 cm longer than Ian's candle. Tom's candle and Ian'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, Ian's candle was burnt out while Tom's candle was burnt out at 1. Find the original height of each candle.
(a) Ian's candle
(b) Tom's candle
| |
Tom |
Ian |
Comparing the heights
of candles |
15 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 Tom's candle burning → 2.5 hours of Ian's candle burning
10 hours of Tom's candle burning → 5 hours of Ian's candle burning
Time taken for Ian's candle to burn 15 cm in height
= 5 - 2
= 3 h
3 hours of Ian's candle burning → 15 cm
1 hour of Ian's candle burning → 15 ÷ 3 = 5 cm
Total time taken for Ian's candle to burn
= 2.5 + 2
= 4.5 h
4.5 hours of Ian's candle burning
= 4.5 x 5
= 22.5 cm
Original height of Ian's candle = 22.5 cm
(b)
Original height of Tom's candle
= 22.5 + 15
= 37.5 cm
Answer(s): (a) 22.5 cm; (b) 37.5 cm
