Question

a $6\frac{1}{4}$-inch candle burns down in 5 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.

Explanation:

Step1: Find the burning rate per hour

The candle is \(6\frac{1}{4}\) inches, which is \(\frac{25}{4}\) inches, and it burns down in 5 hours. The rate \(r\) is total length divided by total time, so \(r=\frac{\frac{25}{4}}{5}\). Simplifying, \(\frac{25}{4}\div5=\frac{25}{4}\times\frac{1}{5}=\frac{5}{4}\) inches per hour.

Step2: Write the proportional equation

Since the amount burned \(b\) is proportional to time \(t\) with rate \(\frac{5}{4}\), the equation is \(b = \frac{5}{4}t\).

Answer:

\(b=\frac{5}{4}t\)