Question

An 8-inch small candle burns 1/4 inch every hour. A 12-inch large candle burns 1/3 inch every hour. After how many hours will the two candles be the same height?

a) 2 hours
b) 3 hours
c) 4 hours
d) 5 hours

Answer 1

The two candles will be the same height after 4 hours when equalizing their respective rates of decrease over time; the 8-inch candle burning at 1/4 inch per hour, and the 12-inch candle burning at 1/3 inch per hour. The correct option is c.

Step-by-step explanation:

The question at hand is a problem of equalizing two rates of change over time. We have two candles; the first is an 8-inch candle that burns at a rate of 1/4 inch per hour, and the second is a 12-inch candle that burns at a rate of 1/3 inch per hour. To find the time it takes for both candles to be the same height, we need to set up an equation where both of their heights minus their respective rates of burning times the number of hours (t) are equal.

Let's denote the height of the small candle after t hours as S(t) and the height of the large candle as L(t). Initially, S(0) = 8 inches and L(0) = 12 inches.
We set S(t) equal to L(t) and solve for the time t:
8 - (1/4)t = 12 - (1/3)t.

To solve the equation, we find a common denominator for the fractions, which is 12, and rewrite the equation as 32 - 3t = 36 - 4t. The solution to this equation gives us t = 4 hours. Hence, after 4 hours, both candles will be the same height. Hence, c is the correct option.