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The question in the image asks to prove that the distance traveled on uphill and downhill sections does not affect the average fuel consumption rate if both distances are equal. It then requests identifying the correct formula for the average fuel consumption rate \( r_{\text{avg}} \).

Let's break this down.

### Known Information:
- A truck consumes fuel at different rates based on the terrain:
  - **Uphill**: It consumes 1 liter for every 5 km (fuel consumption rate \( r_1 \)).
  - **Downhill**: It consumes 1 liter for every 30 km (fuel consumption rate \( r_2 \)).
  - For level roads, it uses 1 liter for every 10 km.

The task is to prove that the distance of uphill and downhill segments doesn't affect the average fuel consumption rate as long as the distances are equal.

### Formula:
When the distances are the same for two segments (uphill and downhill), the average rate can be found using the harmonic mean of the two rates, as fuel consumption works inversely to distance rates.

The harmonic mean formula for two rates is:

\[
r_{\text{avg}} = \frac{2r_1r_2}{r_1 + r_2}
\]

Where:
- \( r_1 \) is the fuel rate for uphill,
- \( r_2 \) is the fuel rate for downhill.

Given this, let me know if you'd like any additional details or further explanation.

### Relative Questions:
1. How does the harmonic mean apply to rates and distances?
2. Can you explain why the arithmetic mean would not be suitable for this case?
3. How can we calculate the average fuel consumption if the distances uphill and downhill were different?
4. Would the average fuel consumption be affected if the truck carried a load?
5. How does the rate change for different terrains affect fuel consumption?

**Tip**: Always check whether you're dealing with rates or quantities. For rates, harmonic means are usually more appropriate when averaging!

Buktikan bahwa jarak tempuh pada lintasan menanjak dan menurun tidak akan memengaruhi rata-rata bahan bakar yang dihabiskan asalkan jarak keduanya sama. Rumus yang tepat untuk menyatakan rata-rata bahan bakar (r_avg) yang dihabiskan pada jarak yang sama adalah:

Learn how to prove that traveling the same distance uphill and downhill does not affect the average fuel consumption. This problem demonstrates the use of the harmonic mean formula, r_avg = 2r_1r_2 / (r_1 + r_2), for calculating fuel efficiency. Suitable for high school students.

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