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