A 3 1/2 inch candle burns down in 7 hours. Assuming the candles are the same thickness and make (that is directly proportional,) how long would it take a 2 1/2 inch candle to burn down?
Let's use the concept of "lengths" to solve this problem.
If a 3 1/2 inch candle burns down in 7 hours, we can say that the candle burns at a rate of 3 1/2 inches per 7 hours, or simplifying, 1/2 inch per hour.
Since the thickness of the candles is the same and they burn at the same rate (directly proportional), we can set up a proportion to find the time it would take for a 2 1/2 inch candle to burn down:
(2 1/2 inches) / (x hours) = (3 1/2 inches) / (7 hours)
To solve for x, we cross-multiply:
(2 1/2 inches) * (7 hours) = (3 1/2 inches) * (x hours)
Simplifying both sides:
(5/2) * (7) = (7/2) * x
35/2 = 7/2 * x
Now, divide both sides by 7/2 to solve for x:
(35/2) / (7/2) = x
35/2 * 2/7 = x
35/7 = x
5 = x
Therefore, it would take a 2 1/2 inch candle 5 hours to burn down.