A reconnaissance plane flies 679 km away from
its base at 826 m/s, then flies back to its base
at 1239 m/s.
What is its average speed?
Answer in units of m/s.

To find the average speed of the reconnaissance plane, we need to calculate the total distance it travels and divide that by the total time taken for the entire journey.

### Step-by-Step Solution

1. **Calculate the total distance traveled:**

   The plane flies 679 km away from its base and then flies back the same distance.

   \[
   \text{Total distance} = 679 \, \text{km} + 679 \, \text{km} = 1358 \, \text{km}
   \]

   Convert the distance from kilometers to meters:

   \[
   1358 \, \text{km} \times 1000 \, \text{m/km} = 1,358,000 \, \text{m}
   \]

2. **Calculate the time taken for each leg of the journey:**

   - Time to travel away from the base at 826 m/s:

   \[
   t_1 = \frac{\text{Distance}}{\text{Speed}} = \frac{679,000 \, \text{m}}{826 \, \text{m/s}}
   \]

   - Time to return to the base at 1239 m/s:

   \[
   t_2 = \frac{\text{Distance}}{\text{Speed}} = \frac{679,000 \, \text{m}}{1239 \, \text{m/s}}
   \]

3. **Calculate the total time for the round trip:**

   \[
   t_{\text{total}} = t_1 + t_2
   \]

   Let's compute \( t_1 \) and \( t_2 \) first:

   \[
   t_1 = \frac{679,000}{826} \approx 822 \, \text{s}
   \]
   
   \[
   t_2 = \frac{679,000}{1239} \approx 548 \, \text{s}
   \]

   Then, the total time \( t_{\text{total}} \) is:

   \[
   t_{\text{total}} = 822 + 548 = 1370 \, \text{s}
   \]

4. **Calculate the average speed:**

   The average speed is the total distance divided by the total time:

   \[
   \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{1,358,000 \, \text{m}}{1370 \, \text{s}}
   \]

   Calculate the average speed:

   \[
   \text{Average speed} \approx 991.24 \, \text{m/s}
   \]

### Final Answer

The average speed of the reconnaissance plane is approximately **991.24 m/s**.

Would you like more details on any step or have any other questions?

Here are 5 related questions for further exploration:

1. How would the average speed change if the plane's speed on the return trip was increased to 1500 m/s?
2. What is the formula for calculating average speed in general cases involving different speeds?
3. How does the difference in speeds for each leg of the journey affect the overall average speed?
4. If the distance to the base was doubled, how would the average speed calculation change?
5. What are the implications of using average speed instead of instantaneous speed in aviation?

**Tip:** When dealing with problems involving average speed, always remember that it depends on the total distance and total time, not just a simple average of speeds.

Learn how to calculate the average speed of a reconnaissance plane that travels 679 km away from its base at different speeds. This problem involves concepts from physics, specifically kinematics and average speed calculations. Suitable for high school students studying physics.

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