During Christmas, Riordan's candle and Xavier's candle were placed on an altar. Riordan's candle was 8 cm longer than Xavier's candle. Riordan's candle and Xavier'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, Xavier's candle was burnt out while Riordan's candle was burnt out at 1. Find the original height of each candle.
(a) Xavier's candle
(b) Riordan's candle
|
Riordan |
Xavier |
Comparing the heights of candles |
8 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 Riordan's candle burning → 2.5 hours of Xavier's candle burning
10 hours of Riordan's candle burning → 5 hours of Xavier's candle burning
Time taken for Xavier's candle to burn 8 cm in height
= 5 - 1
= 4 h
4 hours of Xavier's candle burning → 8 cm
1 hour of Xavier's candle burning → 8 ÷ 4 = 2 cm
Total time taken for Xavier's candle to burn
= 2.5 + 1
= 3.5 h
3.5 hours of Xavier's candle burning
= 3.5 x 2
= 7 cm
Original height of Xavier's candle = 7 cm
(b)
Original height of Riordan's candle
= 7 + 8
= 15 cm
Answer(s): (a) 7 cm; (b) 15 cm