To find out how many minutes it will take Javier to jog 1 mile, we first need to determine his pace in minutes per mile based on the information provided.
Javier jogs \( \frac{3}{4} \) of a mile in \( 8 \frac{1}{2} \) minutes.
First, convert \( 8 \frac{1}{2} \) to an improper fraction or a decimal: \[ 8 \frac{1}{2} = 8 + \frac{1}{2} = 8.5 \text{ minutes} \]
Now, we know that he jogs \( \frac{3}{4} \) mile in \( 8.5 \) minutes. To find out how many minutes it takes to jog 1 mile, we can set up a proportion:
\[ \text{Time for 1 mile} = \frac{8.5 \text{ minutes}}{\frac{3}{4} \text{ miles}} \times 1 \text{ mile} \]
Calculating this gives: \[ \text{Time for 1 mile} = 8.5 \div \frac{3}{4} = 8.5 \times \frac{4}{3} = \frac{8.5 \times 4}{3} \]
Now, calculating \( 8.5 \times 4 \): \[ 8.5 \times 4 = 34 \]
Now divide by 3: \[ \frac{34}{3} \approx 11.33 \text{ minutes} \]
Therefore, it will take Javier approximately \( 11.33 \) minutes, or \( 11 \frac{1}{3} \) minutes, to jog 1 mile at the same pace.
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