Let's solve the problem from the image.

Problem Breakdown:

• A 360 m long train runs at 108 km/h and crosses another train running in the opposite direction at 90 km/h.
• The crossing (i.e., time taken to pass each other completely) happens in 12 seconds.
• We need to find the length of the second train.

Step-by-Step Solution:

1. Relative Speed: Since the trains are moving in opposite directions, the relative speed is the sum of their speeds. $\text{Relative Speed} = 108 \, \text{km/h} + 90 \, \text{km/h} = 198 \, \text{km/h}$ Convert this speed into meters per second: $\text{Relative Speed} = 198 \times \frac{1000}{3600} = 55 \, \text{m/s}$

2. Distance Covered in 12 seconds: The total distance covered when the two trains cross each other is the sum of their lengths. Let $L$ be the length of the second train. The distance covered in 12 seconds is: $\text{Distance} = \text{Relative Speed} \times \text{Time}$ $\text{Distance} = 55 \, \text{m/s} \times 12 \, \text{s} = 660 \, \text{m}$

3. Forming the Equation: The sum of the lengths of the two trains must equal the distance covered, which is 660 m. We know the length of the first train is 360 m: $360 \, \text{m} + L = 660 \, \text{m}$ $L = 660 \, \text{m} - 360 \, \text{m} = 300 \, \text{m}$

Thus, the length of the other train is 300 meters.

Would you like further details or have any questions?

Here are some related questions to think about:

1. How would the solution change if the second train was moving in the same direction?
2. What happens to the crossing time if the speeds of the trains increase?
3. How does the relative speed affect the time taken to cross if the length of the trains is doubled?
4. What formula would you use if the time was measured in minutes instead of seconds?
5. How can you convert the speeds into miles per hour (mph)?

Tip: Always ensure to convert units properly when calculating speeds and distances, especially when dealing with different measurement systems like kilometers per hour and meters per second.