During Christmas, Sam's candle and Tim's candle were placed on an altar. Sam's candle was 12 cm longer than Tim's candle. Sam's candle and Tim'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, Tim's candle was burnt out while Sam's candle was burnt out at 1. Find the original height of each candle.
(a) Tim's candle
(b) Sam's candle
| |
Sam |
Tim |
Comparing the heights
of candles |
12 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 Sam's candle burning → 2.5 hours of Tim's candle burning
10 hours of Sam's candle burning → 5 hours of Tim's candle burning
Time taken for Tim's candle to burn 12 cm in height
= 5 - 3
= 2 h
2 hours of Tim's candle burning → 12 cm
1 hour of Tim's candle burning → 12 ÷ 2 = 6 cm
Total time taken for Tim's candle to burn
= 2.5 + 3
= 5.5 h
5.5 hours of Tim's candle burning
= 5.5 x 6
= 33 cm
Original height of Tim's candle = 33 cm
(b)
Original height of Sam's candle
= 33 + 12
= 45 cm
Answer(s): (a) 33 cm; (b) 45 cm
