A 1, one half1
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1
-inch candle burns down in 6 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.
The proportional equation for b in terms of t that matches the context is:
b = (1/6)t
This equation states that the amount of the candle burned, b, is equal to one-sixth (or one divided by six) of the time, t, in hours.
To write a proportional equation for the amount of candle burned, b, in terms of time, t, we can use the given information that a 1 and one-half inch candle burns down in 6 hours.
First, let's determine the rate at which the candle burns. We can divide the length of the candle, 1 and one-half inch, by the time it takes to burn, 6 hours:
Rate = Length of candle / Time taken = 1.5 inches / 6 hours = 0.25 inches/hour
This means that the candle burns at a rate of 0.25 inches per hour.
Now, we can write the proportional equation for the amount of the candle burned, b, in terms of time, t:
b = Rate * t
Substituting the rate we found earlier, the equation becomes:
b = 0.25t
Therefore, the proportional equation that represents the amount of the candle burned, b, in terms of time, t, is:
b = 0.25t
To write a proportional equation for b in terms of t, we can use the information provided in the question. We know that a 1 1/2 -inch candle burns down in 6 hours.
Let's represent the length of the candle burned, b, in inches, and the time passed, t, in hours.
Since the candle burns down linearly, we can set up a proportion using the given values and solve for the constant of proportionality.
The length of the candle burned, b, is proportional to the time passed, t.
b/t = (1 1/2 inches) / (6 hours)
To simplify the fraction 1 1/2, we can convert it to an improper fraction:
b/t = (3/2 inches) / (6 hours)
Now, we can cross-multiply and solve for b:
b * 6 = 3/2 * t
Multiply both sides by 2/3 to isolate b:
b = (2/3) * (3/2) * t
b = (2/3) * t
Therefore, the proportional equation for b in terms of t is:
b = (2/3) * t