Question

A 12-inch candle and an 18-inch candle are lit at the same time. The 12 inch candle burns 3/4 inches every hour. The 18-inch candle burns 3 inches every hour.

How much time will it take for the candles to burn down to the same height?

Answer 1

It will take approximately 2.67 hours for a 12-inch candle burning at 3/4 inches per hour and an 18-inch candle burning at 3 inches per hour to burn down to the same height after setting up the equation 12 - (3/4)t = 18 - 3t and solving for t.

Step-by-step explanation:

To determine how long it will take for the 12-inch candle and the 18-inch candle to burn down to the same height, we can set up a simple equation based on the burn rates of the candles. The 12-inch candle burns at a rate of 3/4 inches every hour, and the 18-inch candle burns at a rate of 3 inches every hour.

Let's denote t as the time in hours it takes for both candles to be the same height. The amount of candle left can be represented as the initial height of the candle minus the burn rate times time, t.

For the 12-inch candle: 12 - (3/4)t
For the 18-inch candle: 18 - 3t

We set them equal to solve for t:

12 - (3/4)t = 18 - 3t

Multiplying through by 4 to clear the fraction gives us:

48 - 3t = 72 - 12t

Now, add 12t to both sides and subtract 48 from both sides to isolate t:

9t = 24

Divide both sides by 9 to find t:

t = 24/9

t = 2.67 hours

Therefore, it will take approximately 2.67 hours for both candles to reach the same height.