Since the amount of time Mr. Jones jogs is inversely proportional to his jogging rate, we can express this relationship mathematically as:
\[ \text{Time} \times \text{Rate} = k \]
where \( k \) is a constant.
To provide possible rates and times for two of his jogs, we need values for the time and rate that maintain this relationship. Let's assume the following pairs:
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Jog 1:
- Rate: 4 miles per hour
- Time: 30 minutes (0.5 hours)
Here, \( k = 4 \text{ mph} \times 0.5 \text{ h} = 2 \text{ miles} \).
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Jog 2:
- Rate: 6 miles per hour
- Time: 20 minutes (1/3 hours)
Similarly, \( k = 6 \text{ mph} \times \frac{1}{3} \text{ h} = 2 \text{ miles} \).
Both jogs yield the same value for \( k \), confirming the inverse relationship.
So, one possible set of rates and times is:
- Rate: 4 mph, Time: 30 minutes
- Rate: 6 mph, Time: 20 minutes
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