Train Speed Calculation

The problem asks us to find the time taken by a train of a specific length to cross a bridge of a different length. We are given information about the train crossing one bridge and asked to calculate the time for crossing another.

First, let's list the given information:

• Length of the train: 210 metres
• Time taken to cross a bridge of length 540 metres: 25 seconds
• Length of the second bridge: 630 metres

To solve this problem, we need to calculate the speed of the train first. The speed of the train is constant throughout the journey.

When a train crosses a bridge, the total distance covered by the train is equal to the sum of the length of the train and the length of the bridge.

For the first bridge crossing:

• Length of train = 210 m
• Length of the first bridge = 540 m
• Total distance covered = Length of train + Length of the first bridge
• Total distance = 210 m + 540 m = 750 m
• Time taken = 25 s

The relationship between speed, distance, and time is given by the formula:

$ \text{Speed} = \frac{\text{Distance}}{\text{Time}} $

Now, we calculate the train's speed:

$ \text{Speed} = \frac{750 \text{ m}}{25 \text{ s}} $

$ \text{Speed} = 30 \text{ m/s} $

So, the speed of the train is 30 metres per second.

Time to Cross Second Bridge Calculation

Now that we have the speed of the train, we can calculate the time it will take to cross the second bridge.

For the second bridge crossing:

• Length of train = 210 m
• Length of the second bridge = 630 m
• Total distance to be covered = Length of train + Length of the second bridge
• Total distance = 210 m + 630 m = 840 m
• Speed of the train = 30 m/s (as calculated above)

We use the same formula, rearranged to find time:

$ \text{Time} = \frac{\text{Distance}}{\text{Speed}} $

Calculating the time taken for the second bridge:

$ \text{Time} = \frac{840 \text{ m}}{30 \text{ m/s}} $

$ \text{Time} = 28 \text{ s} $

Therefore, the train will take 28 seconds to cross the 630 metres long bridge.

Final Time Calculation

The calculation shows that the train takes 28 seconds to cross the 630 metres long bridge.