During Christmas, Justin's candle and Mark's candle were placed on an altar. Justin's candle was 6 cm longer than Mark's candle. Justin's candle and Mark'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, Mark's candle was burnt out while Justin's candle was burnt out at 1. Find the original height of each candle.
(a) Mark's candle
(b) Justin's candle
| |
Justin |
Mark |
Comparing the heights
of candles |
6 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 Justin's candle burning → 2.5 hours of Mark's candle burning
10 hours of Justin's candle burning → 5 hours of Mark's candle burning
Time taken for Mark's candle to burn 6 cm in height
= 5 - 3
= 2 h
2 hours of Mark's candle burning → 6 cm
1 hour of Mark's candle burning → 6 ÷ 2 = 3 cm
Total time taken for Mark's candle to burn
= 2.5 + 3
= 5.5 h
5.5 hours of Mark's candle burning
= 5.5 x 3
= 16.5 cm
Original height of Mark's candle = 16.5 cm
(b)
Original height of Justin's candle
= 16.5 + 6
= 22.5 cm
Answer(s): (a) 16.5 cm; (b) 22.5 cm
