Question

A 13 3/4 -inch candle burns down in 11 hours. If b represents how much of the candle, in inches, has burned away at any time given in hours, t, write a proportional equation for b in terms of t that matches the context.

Answer 1

To create a proportional equation for a candle that burns down at a constant rate, you divide the initial length of the candle by the time it takes to burn completely, which gives the hourly burn rate. The resulting equation representing how much of the candle has burned, b, in terms of time in hours, t, is b = 1.25t.

Step-by-step explanation:

To write a proportional equation for b in terms of t, we need to understand that the candle’s length decreases at a constant rate as it burns over time. The total length of the candle is 13 3/4 inches and it completely burns out in 11 hours. Therefore, the rate at which the candle burns can be calculated by dividing its total length by the total time of burning. This gives us the rate of 13.75 inches / 11 hours or 1.25 inches per hour.

Using this information, the equation that represents how much of the candle has burned away at any given time t can be represented as:

b = 1.25t

This equation implies that the amount of candle burned, b, is equal to 1.25 times the number of hours, t, that have passed.

Answer 2

5t = 4b

Step-by-step explanation:

Here, we want to write a proportional relationship for b in terms of t

From the question, b represent the amount of candle burned away in a given time t hours

From what we have initially, 13 3/4 burnt in 11 hours

So in 1 hour, the amount burnt will be;

55/4/11 = 5/4

5/4 inches of candle burnt in 1 hour

5/4 inches = b/t

So b inches burnt in t hours

5/4 = b/t

5t = 4b