Let's break down the problem step by step:

• The first train leaves the station at 2 PM with a speed of 60 km/h.
• The second train leaves the station at 3 PM with a speed of 90 km/h.

Step 1: Calculate the distance the first train covers before the second train starts.

The first train has a 1-hour head start (from 2 PM to 3 PM) and is traveling at 60 km/h.

Distance covered by the first train in 1 hour: $\text{Distance} = \text{Speed} \times \text{Time} = 60 \, \text{km/h} \times 1 \, \text{hour} = 60 \, \text{km}$

So, at 3 PM, when the second train starts, the first train is already 60 km ahead.

Step 2: Relative speed between the two trains.

• The second train travels faster than the first one, so the relative speed between them is: $\text{Relative speed} = 90 \, \text{km/h} - 60 \, \text{km/h} = 30 \, \text{km/h}$

Step 3: Calculate the time it takes for the second train to catch up.

The second train needs to cover the 60 km gap at a relative speed of 30 km/h. The time it will take to catch up is given by: $\text{Time} = \frac{\text{Distance}}{\text{Relative speed}} = \frac{60 \, \text{km}}{30 \, \text{km/h}} = 2 \, \text{hours}$

Conclusion:

It will take 2 hours for the second train to catch up with the first one. Therefore, the second train will catch up at 5 PM.

Let me know if you need further details or clarifications!

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Here are 5 related questions to consider:

1. How can relative speed be applied to more complex problems involving multiple moving objects?
2. What happens if the second train starts before the first train, how does the outcome change?
3. How does the time it takes to catch up change if the first train travels at a different speed?
4. If the first train were to stop, how could you calculate the second train's time to cover the remaining distance?
5. What are real-life scenarios where calculating relative speed is important?

Tip: When solving relative speed problems, always start by determining the time difference and speeds involved.