During Christmas, Oscar's candle and Riordan's candle were placed on an altar. Oscar's candle was 24 cm longer than Riordan's candle. Oscar's candle and Riordan'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, Riordan's candle was burnt out while Oscar's candle was burnt out at 1. Find the original height of each candle.
(a) Riordan's candle
(b) Oscar's candle
| |
Oscar |
Riordan |
Comparing the heights
of candles |
24 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 Oscar's candle burning → 2.5 hours of Riordan's candle burning
10 hours of Oscar's candle burning → 5 hours of Riordan's candle burning
Time taken for Riordan's candle to burn 24 cm in height
= 5 - 1
= 4 h
4 hours of Riordan's candle burning → 24 cm
1 hour of Riordan's candle burning → 24 ÷ 4 = 6 cm
Total time taken for Riordan's candle to burn
= 2.5 + 1
= 3.5 h
3.5 hours of Riordan's candle burning
= 3.5 x 6
= 21 cm
Original height of Riordan's candle = 21 cm
(b)
Original height of Oscar's candle
= 21 + 24
= 45 cm
Answer(s): (a) 21 cm; (b) 45 cm
