During Christmas, Tim's candle and Nick's candle were placed on an altar. Tim's candle was 12 cm longer than Nick's candle. Tim's candle and Nick'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, Nick's candle was burnt out while Tim's candle was burnt out at 1. Find the original height of each candle.
(a) Nick's candle
(b) Tim's candle
|
Tim |
Nick |
Comparing the heights of candles |
12 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 Tim's candle burning → 2.5 hours of Nick's candle burning
10 hours of Tim's candle burning → 5 hours of Nick's candle burning
Time taken for Nick's candle to burn 12 cm in height
= 5 - 1
= 4 h
4 hours of Nick's candle burning → 12 cm
1 hour of Nick's candle burning → 12 ÷ 4 = 3 cm
Total time taken for Nick's candle to burn
= 2.5 + 1
= 3.5 h
3.5 hours of Nick's candle burning
= 3.5 x 3
= 10.5 cm
Original height of Nick's candle = 10.5 cm
(b)
Original height of Tim's candle
= 10.5 + 12
= 22.5 cm
Answer(s): (a) 10.5 cm; (b) 22.5 cm