During Christmas, Sean's candle and Justin's candle were placed on an altar. Sean's candle was 4 cm longer than Justin's candle. Sean's candle and Justin'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, Justin's candle was burnt out while Sean's candle was burnt out at 1. Find the original height of each candle.
(a) Justin's candle
(b) Sean's candle
| |
Sean |
Justin |
Comparing the heights
of candles |
4 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 Sean's candle burning → 2.5 hours of Justin's candle burning
10 hours of Sean's candle burning → 5 hours of Justin's candle burning
Time taken for Justin's candle to burn 4 cm in height
= 5 - 3
= 2 h
2 hours of Justin's candle burning → 4 cm
1 hour of Justin's candle burning → 4 ÷ 2 = 2 cm
Total time taken for Justin's candle to burn
= 2.5 + 3
= 5.5 h
5.5 hours of Justin's candle burning
= 5.5 x 2
= 11 cm
Original height of Justin's candle = 11 cm
(b)
Original height of Sean's candle
= 11 + 4
= 15 cm
Answer(s): (a) 11 cm; (b) 15 cm
