During Christmas, Liam's candle and Tom's candle were placed on an altar. Liam's candle was 12 cm longer than Tom's candle. Liam's candle and Tom'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, Tom's candle was burnt out while Liam's candle was burnt out at 1. Find the original height of each candle.
(a) Tom's candle
(b) Liam's candle
|
Liam |
Tom |
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 Liam's candle burning → 2.5 hours of Tom's candle burning
10 hours of Liam's candle burning → 5 hours of Tom's candle burning
Time taken for Tom's candle to burn 12 cm in height
= 5 - 3
= 2 h
2 hours of Tom's candle burning → 12 cm
1 hour of Tom's candle burning → 12 ÷ 2 = 6 cm
Total time taken for Tom's candle to burn
= 2.5 + 3
= 5.5 h
5.5 hours of Tom's candle burning
= 5.5 x 6
= 33 cm
Original height of Tom's candle = 33 cm
(b)
Original height of Liam's candle
= 33 + 12
= 45 cm
Answer(s): (a) 33 cm; (b) 45 cm