Question

a 8\frac{1}{4}-inch candle burns down in 11 hours. how far has it burned after 10\frac{1}{2} hours? enter a whole number, improper fraction, or use the mixed number button to enter your answer as a mixed number.
answer attempt 1 out of 2
answer: in.
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mixed number

Explanation:

Step1: Convert mixed - numbers to improper fractions

The length of the candle is $8\frac{1}{4}=\frac{8\times4 + 1}{4}=\frac{33}{4}$ inches, and the time is $10\frac{1}{2}=\frac{10\times2+1}{2}=\frac{21}{2}$ hours, and the total burning time is 11 hours.

Step2: Find the rate of burning

The rate of burning of the candle is $\text{Rate}=\frac{\text{Length of candle}}{\text{Total burning time}}$. So the rate $r=\frac{\frac{33}{4}}{11}=\frac{33}{4}\times\frac{1}{11}=\frac{3}{4}$ inches per hour.

Step3: Calculate the length burned

The length burned $L$ after $\frac{21}{2}$ hours is $L = r\times t$, where $r=\frac{3}{4}$ inches per hour and $t = \frac{21}{2}$ hours. So $L=\frac{3}{4}\times\frac{21}{2}=\frac{63}{8}=7\frac{7}{8}$ inches.

Answer:

$7\frac{7}{8}$