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The image contains a problem related to the speed-time behavior of a cross-country runner training for a marathon, with parts (a) through (d) posing various mathematical questions. Here's a breakdown of the problem:

### Problem:
A cross-country runner's training involves varying speeds and periods of acceleration and deceleration. His running schedule for today is:
1. **Jogging for 10 minutes** at 5 miles per hour.
2. **Accelerating for 1 minute** to reach 10 miles per hour.
3. **Running at 10 miles per hour** for 5 minutes.
4. **Decelerating for 1 minute** to reach 7 miles per hour.
5. **Running at 7 miles per hour** for 30 minutes.
6. **Decelerating for 2 minutes** to 3 miles per hour.
7. **Running at 3 miles per hour** for 10 minutes before stopping.

#### Tasks:
- **(a)** Make a speed vs. time graph representing this situation.
- **(b)** Find the instantaneous rate of change in the runner’s speed at 10.5 minutes.
- **(c)** Calculate the average rate at which he changed speeds from minute 11 to minute 49.
- **(d)** Explain why the answer for part (c) doesn’t fully represent the speed change in the runner's training between minute 11 and minute 49.

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A cross-country runner is training for a marathon. His training program requires him to run at different speeds for different lengths of time. His program also requires him to accelerate and decelerate at a constant rate. Today he begins by jogging for 10 min at a rate of 5 miles per hour. He then spends 1 min accelerating to a rate of 10 miles per hour. He stays at this rate for 5 min. He then decelerates for 1 min to a rate of 7 miles per hour. He stays at this rate for 30 min. Finally, to cool down, he decelerates for 2 min to a rate of 3 miles per hour. He stays at this rate for a final 10 min and then stops.

Solve a cross-country runner's speed-time problem with varying speeds, including calculating instantaneous and average rates of change. Suitable for high school students covering rate of change, speed-time graphs, and calculus concepts.

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