Questions: Mr. Jones jogs the same route each day. The amount of time he jogs is inversely proportional to his jogging rate. What option gives possible rates and times for two of his jogs? 6 mph for 1.5 hours and 5 mph for 1.25 hours 4 mph for 2.25 hours and 6 mph for 1.5 hours 4.5 mph for 3 hours and 6 mph for 4 hours 5 mph for 2 hours and 4 mph for 3 hours

Solution Steps

To determine which option gives possible rates and times for Mr. Jones's jogs, we need to verify the inverse proportionality between time and rate. This means that the product of the rate and time should be constant for each jog. We will calculate the product of rate and time for each option and check if they are equal.

We have the following options for Mr. Jones's jogging rates and times:

1. \( (6 \text{ mph}, 1.5 \text{ hours}, 5 \text{ mph}, 1.25 \text{ hours}) \)
2. \( (4 \text{ mph}, 2.25 \text{ hours}, 6 \text{ mph}, 1.5 \text{ hours}) \)
3. \( (4.5 \text{ mph}, 3 \text{ hours}, 6 \text{ mph}, 4 \text{ hours}) \)
4. \( (5 \text{ mph}, 2 \text{ hours}, 4 \text{ mph}, 3 \text{ hours}) \)

We need to check if the product of rate and time is constant for each option. The condition for inverse proportionality is given by: \[ \text{Rate} \times \text{Time} = k \quad \text{(constant)} \]

Calculating for each option:

1. For option 1: \( 6 \times 1.5 = 9 \) and \( 5 \times 1.25 = 6.25 \) (not equal)
2. For option 2: \( 4 \times 2.25 = 9 \) and \( 6 \times 1.5 = 9 \) (equal)
3. For option 3: \( 4.5 \times 3 = 13.5 \) and \( 6 \times 4 = 24 \) (not equal)
4. For option 4: \( 5 \times 2 = 10 \) and \( 4 \times 3 = 12 \) (not equal)

From the calculations, only option 2 satisfies the condition of inverse proportionality, as both products equal \( 9 \).

Final Answer