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This problem involves related rates, specifically concerning the shadow length created by a light pole as a person walks away from it.

### Given:
1. Height of pole = 26 ft
2. Height of girl = 4 ft
3. Girl's walking speed = 3 ft/sec
4. Distance between the girl and the pole = 22 ft when we need to calculate the rates.

### Solution Outline:
1. **Set up the geometry**:
   - Since the light source is directly above the pole, this situation creates similar triangles: one with the pole and the tip of the shadow, and the other with the girl and the tip of her shadow.

2. **Define Variables**:
   - Let \( x \) be the distance of the girl from the pole (given as 22 ft).
   - Let \( s \) be the length of her shadow.
   - The rate at which she is walking, \( \frac{dx}{dt} = 3 \) ft/sec.

3. **Use Similar Triangles**:
   - By setting up similar triangles, we have:
     \[
     \frac{26}{x + s} = \frac{4}{s}
     \]
   - Cross-multiplying gives:
     \[
     26s = 4(x + s)
     \]
     \[
     26s = 4x + 4s
     \]
     \[
     22s = 4x
     \]
     \[
     s = \frac{2x}{11}
     \]

4. **Differentiate with respect to time**:
   - Differentiate both sides with respect to \( t \) to find \( \frac{ds}{dt} \):
     \[
     \frac{ds}{dt} = \frac{2}{11} \cdot \frac{dx}{dt}
     \]
   - Substitute \( \frac{dx}{dt} = 3 \) ft/sec:
     \[
     \frac{ds}{dt} = \frac{2}{11} \cdot 3 = \frac{6}{11} \approx 0.545 \text{ ft/sec}
     \]

5. **Find the rate at which the tip of her shadow is moving**:
   - The tip of her shadow is at a distance of \( x + s \) from the pole.
   - Differentiate \( x + s \) with respect to \( t \):
     \[
     \frac{d}{dt}(x + s) = \frac{dx}{dt} + \frac{ds}{dt}
     \]
   - Substitute the values:
     \[
     \frac{d}{dt}(x + s) = 3 + 0.545 = 3.545 \text{ ft/sec}
     \]

### Answer:
- **The rate at which the tip of her shadow is moving away from the pole**: \( \approx 3.545 \) ft/sec.

Would you like more details on any part of this solution?

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### Follow-up Questions:
1. How would the result change if the girl’s walking speed increased?
2. What if the height of the pole were different?
3. Could you set up an equation to model how the shadow length changes over time?
4. How does this problem relate to real-world applications involving similar triangles?
5. Could this approach be adapted if the girl were moving toward the pole instead?

### Tip:
When working with related rates problems, always start by clearly defining all variables and their relationships using geometry (often similar triangles) before differentiating.

A street light is at the top of a 26 ft pole. A 4 ft tall girl walks along a straight path away from the pole with a speed of 3 ft/sec. At what rate is the tip of her shadow moving away from the light (i.e., away from the top of the pole) when the girl is 22 ft away from the pole?

Solve a related rates problem involving a 26 ft street light and a 4 ft tall girl walking away at 3 ft/sec. Calculate the rate at which the tip of her shadow moves away from the pole when she is 22 ft away. Explore similar triangles and differentiation.

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