A train is going on a journey. First it travels east for 50 kilometers. Then it turns north and travels for 22 kilometers. Next it goes west for 50 kilometers. Finally, it travels south for a certain number of kilometers. At the end of its journey it is back at its original location. How many kilometers did it travel in the southward direction?


We are asked to find how many kilometers the train traveled in the southward direction to return to its original location. Here's the breakdown of the train's journey step by step:

1. **Eastward Movement**: The train first travels east for 50 kilometers.
2. **Northward Movement**: Then, it turns north and travels for 22 kilometers.
3. **Westward Movement**: After that, it moves west for 50 kilometers.
4. **Southward Movement**: Finally, the train moves south by an unknown distance, \( x \), to return to the starting point.

Let's visualize the train's movements in a coordinate plane:

- The eastward and westward movements cancel each other out because the distance traveled east (50 km) equals the distance traveled west (50 km). Therefore, the net east-west displacement is zero.
- The northward movement is 22 kilometers, and the southward movement is \( x \) kilometers.

For the train to return to its original location, the northward displacement must be canceled out by the southward movement. Thus, the southward distance \( x \) must be equal to the northward distance, which is 22 kilometers.

Therefore, the distance traveled south is:
\[
x = 22 \text{ kilometers}
\]

The train traveled **22 kilometers** in the southward direction.

Would you like further details or have any questions?

### Related Questions:
1. What would happen if the train traveled more kilometers south than north?
2. If the journey distance increased, how would the pattern change?
3. How could we represent this problem geometrically in terms of vectors?
4. What would the net displacement be if the train did not return to its original location?
5. How would the calculation change if the distances traveled east and west were not equal?

**Tip**: Visualizing movement on a coordinate plane can simplify understanding of directional journeys like this one.

A train is going on a journey. First it travels east for 50 kilometers. Then it turns north and travels for 22 kilometers. Next it goes west for 50 kilometers. Finally, it travels south for a certain number of kilometers. At the end of its journey it is back at its original location. How many kilometers did it travel in the southward direction?

Solve a train journey problem where the train travels in multiple directions and returns to its starting point. Learn how to calculate the unknown southward distance using concepts of displacement in coordinate geometry. Suitable for students in Grades 6-8.

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