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The problem describes a scenario where:

- You walk 9 miles at a certain speed.
- Then jog another 9 miles at three times your walking speed.
- The total time spent walking and jogging is 4 hours.

Let:
- \( r \) be the walking speed in miles per hour (mph).
- The jogging speed is \( 3r \) mph.

We can set up the following equations based on the time spent walking and jogging.

1. Time spent walking = \( \frac{9}{r} \) hours.
2. Time spent jogging = \( \frac{9}{3r} = \frac{3}{r} \) hours.

The total time is given as 4 hours:

\[
\frac{9}{r} + \frac{3}{r} = 4
\]

Simplify the equation:

\[
\frac{9 + 3}{r} = 4 \quad \Rightarrow \quad \frac{12}{r} = 4
\]

Solving for \( r \):

\[
r = \frac{12}{4} = 3 \, \text{mph}
\]

Thus, the walking speed is 3 mph, and the jogging speed is:

\[
3r = 3 \times 3 = 9 \, \text{mph}
\]

### Final Answer:
- Walking speed = 3 mph
- Jogging speed = 9 mph

Would you like more details, or do you have any further questions?

Here are five questions to expand your understanding:
1. How would the times change if you increased the total distance for walking and jogging?
2. What happens to the walking and jogging speeds if the total time increases?
3. How can you calculate the average speed for the entire exercise?
4. What is the total distance traveled if you walk and jog for a different amount of time?
5. How would the walking speed change if the jogging speed was no longer three times the walking speed?

**Tip:** Always ensure that the units in your equations match (e.g., miles and hours for speed problems).

As part of an exercise regimen, you walk 9 miles on an indoor track. Then you jog at three times your walking speed for another 9 miles. If the total time spent walking and jogging is 4 hours, find the walking and jogging rates.

Learn how to calculate walking and jogging rates based on a total of 18 miles of walking and jogging in 4 hours. This problem involves algebraic concepts, such as rates and proportions, suitable for students in Grades 8-10.

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