To find out how long it will take Javier to jog 1 mile at his current pace, we first need to determine his pace in minutes per mile based on the information given.
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Determine Javier's pace: He jogs \( \frac{3}{4} \) of a mile in \( 8 \frac{1}{2} \) minutes.
First, convert \( 8 \frac{1}{2} \) to an improper fraction: \[ 8 \frac{1}{2} = 8 + \frac{1}{2} = \frac{16}{2} + \frac{1}{2} = \frac{17}{2} \text{ minutes} \]
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Find the time per mile: If he jogs \( \frac{3}{4} \) of a mile in \( \frac{17}{2} \) minutes, we can find the time it takes to jog 1 mile by setting up a proportion.
Let \( t \) be the time it takes to jog 1 mile.
\[ \frac{3}{4} \text{ mile} \rightleftharpoons \frac{17}{2} \text{ minutes} \] \[ 1 \text{ mile} \rightleftharpoons t \text{ minutes} \]
Using the proportion: \[ \frac{3/4}{1} = \frac{17/2}{t} \]
Cross multiplying gives: \[ 3t = \frac{17}{2} \]
Now, solve for \( t \): \[ t = \frac{17}{2 \cdot 3} = \frac{17}{6} \text{ minutes} \]
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Convert \( \frac{17}{6} \) minutes to a mixed number: Divide \( 17 \) by \( 6 \):
- \( 6 \) goes into \( 17 \) two times (since \( 2 \times 6 = 12 \)).
- The remainder is \( 17 - 12 = 5 \).
Thus, \[ \frac{17}{6} = 2 \frac{5}{6} \text{ minutes} \]
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Final Answer: It will take Javier \( 2 \frac{5}{6} \) minutes to jog 1 mile.
So, the answer is: \[ 2 \frac{5}{6} \]
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