Question

Javier jogs
3
4
of a mile in
8
1
2
minutes.

If he keeps the same pace, how many minutes will it take him to jog
1
mile?

Enter your answer as a mixed number. For example, if your answer is
42
1
2
,
enter 42 1/2

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Answer 1

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.

1. **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:
\[
8 \frac{1}{2} = 8 + \frac{1}{2} = \frac{16}{2} + \frac{1}{2} = \frac{17}{2} \text{ minutes}
\]

2. **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 \( t \):
\[
t = \frac{17}{2 \cdot 3} = \frac{17}{6} \text{ minutes}
\]

3. **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,
\[
\frac{17}{6} = 2 \frac{5}{6} \text{ minutes}
\]

4. **Final Answer:**
It will take Javier \( 2 \frac{5}{6} \) minutes to jog 1 mile.

So, the answer is:
\[
2 \frac{5}{6}
\]