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