A train of certain length traveling with a uniform speed of 36 km `h^(-1)` crosses a bridge of 600 m in 80 s. Find the length of the train.

Answer

To find the length of the train, we can follow these steps:

### Step 1: Convert the speed of the train from km/h to m/s
The speed of the train is given as 36 km/h. We can convert this to meters per second using the conversion factor:
\[ \text{Speed in m/s} = \text{Speed in km/h} \times \frac{5}{18} \]
So,
\[ \text{Speed} = 36 \times \frac{5}{18} = 10 \text{ m/s} \]

### Step 2: Calculate the total distance covered by the train while crossing the bridge
When the train crosses the bridge, it covers a distance equal to the length of the bridge plus the length of the train. We denote the length of the train as \( L \). The total distance covered is:
\[ \text{Total Distance} = \text{Length of the Bridge} + \text{Length of the Train} = 600 \text{ m} + L \]

### Step 3: Use the formula for distance to find the length of the train
We know that distance is equal to speed multiplied by time. The train takes 80 seconds to cross the bridge, so we can express the distance as:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Substituting the known values:
\[ 600 + L = 10 \text{ m/s} \times 80 \text{ s} \]
Calculating the right side:
\[ 600 + L = 800 \text{ m} \]

### Step 4: Solve for the length of the train
Now, we can isolate \( L \):
\[ L = 800 - 600 \]
\[ L = 200 \text{ m} \]

### Conclusion
The length of the train is **200 meters**.

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