Nemo Sum walks from point A to point B and then back again, taking the exact same
path in the opposite direction. Nemo always walks in one of the cardinal directions, i.e.
north, south, east, or west, but not always at the same speed. For reasons known only
to higher powers, Nemo always walks at 4 km/h when going North or South; going East,
Nemo always walks at 3 km/h; and going West, Nemo always walks at 6 km/h.

In this scenario, Nemo Sum walks between points A and B, taking the same path in both directions. His walking speed depends on the direction:

- **North/South**: 4 km/h
- **East**: 3 km/h
- **West**: 6 km/h

To analyze Nemo’s motion, we can approach it step by step:

### 1. **Speed and Distance Breakdown**
   Each segment of the walk can be broken down into four possible directional components: North, South, East, and West. Depending on the distances covered in each direction, we can compute the time taken to walk each leg of the journey.

   Let’s assume:
   - **d_N** is the distance walked North (in kilometers)
   - **d_S** is the distance walked South (in kilometers)
   - **d_E** is the distance walked East (in kilometers)
   - **d_W** is the distance walked West (in kilometers)

   Since Nemo walks from point A to point B and then returns, the total distance walked in each direction is doubled for the round trip.

### 2. **Time Taken**
   The time taken in each direction is calculated by the formula:
   \[
   t = \frac{d}{v}
   \]
   where:
   - \( t \) is the time,
   - \( d \) is the distance,
   - \( v \) is the speed.

   For each segment of the journey:
   - Going **North/South**: The speed is 4 km/h, so the time is \( \frac{d_N}{4} + \frac{d_S}{4} \).
   - Going **East**: The speed is 3 km/h, so the time is \( \frac{d_E}{3} \).
   - Going **West**: The speed is 6 km/h, so the time is \( \frac{d_W}{6} \).

   The total time taken for the round trip would involve summing up the time taken in each direction for both going and returning. Therefore, the total time would be:
   \[
   T_{\text{total}} = 2\left(\frac{d_N}{4} + \frac{d_S}{4} + \frac{d_E}{3} + \frac{d_W}{6}\right)
   \]

### 3. **Total Distance**
   The total distance walked is:
   \[
   D_{\text{total}} = 2(d_N + d_S + d_E + d_W)
   \]

This provides the basic breakdown of how Nemo’s walking speed and time are related to the distances covered in each direction. 

### Follow-up
Do you have any specific values or further details to calculate for Nemo's journey? I can help with solving time, distance, or optimizing the path.

---

Here are 5 related questions for further exploration:
1. What would be the total time taken if Nemo walks 2 km North, 1 km East, and 3 km West?
2. How would the time change if Nemo increased his speed going North?
3. What is the fastest path Nemo could take to minimize the time?
4. How would Nemo’s total time change if he had to stop and rest at the midpoint?
5. Can you calculate the average speed for the entire journey?

**Tip**: Average speed for a round trip can be tricky since it depends on the time spent in each direction, not just the total distance.

Nemo Sum walks from point A to point B and then back again, taking the exact same path in the opposite direction. Nemo always walks in one of the cardinal directions, i.e. north, south, east, or west, but not always at the same speed. For reasons known only to higher powers, Nemo always walks at 4 km/h when going North or South; going East, Nemo always walks at 3 km/h; and going West, Nemo always walks at 6 km/h.

Explore how to calculate the time and distance for Nemo Sum's round trip journey. Analyze directional speeds: 4 km/h North/South, 3 km/h East, and 6 km/h West. Learn key concepts related to speed, time, and distance in this problem, suitable for Grades 9-12 students.

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