Solution to the Problem:
The shorter candle was 11 inches and the longer candle was 12 inches.
Use algebra to solve:
The candles must have different diameters and therefore, different burn rates, because
when they were the same length (at 9 PM), one lasted two hours longer but the other
lasted only 1.5 hours longer.
|
|
Length (inches)
|
Rate (in/hr)
|
Start Time
|
Goes Out at
|
Length (inches)
|
| Longer Candle
|
L + 1
|
x
|
3 PM
|
11 PM
|
8x
|
| Shorter Candle
|
L
|
y
|
5 PM
|
10:30 PM
|
5.5y
|
Now, set up three equations from the table:
(1) (L + 1) - 6x = L - 4y because they are equal at 9 PM
(2) (L + 1) - 8x = 0 because the longer one burns out at 11 PM
(3) L - 5.5y = 0 because the shorter one burns out at 10:30 PM
Solving these three equations,
L = 5.5y
L = 8x - 1
8x - 1 = 5.5y
-6x + 1 = -4y
24x - 3 = 16.5y
-24x + 4 = -16y
1 = .5y
So, y = 2 in/hr.
and the length of the shorter candle is (2 in/hr)(5.5 hr) = 11 inches.
8x - 1 = 11
so x = 3/2 in/hr
and the length of the longer candle is (3/2 in/hr)(8 hr) = 12 inches.