A 180-metre long train crosses another 270-metre long train running in the opposite direction in 10.8 seconds . If the speed of the first train is 60 kmph ,what is the speed of the second train in kmph ?

Options

A. 80
B. 90
C. 150
D. Can't be determined

Explanation

To solve the problem, we need to find the speed of the second train when two trains are crossing each other. Here’s a step-by-step solution:

### Step 1: Understand the problem
We have two trains:
- Train A: 180 meters long, speed = 60 km/h
- Train B: 270 meters long, speed = ? (this is what we need to find)

Both trains are moving in opposite directions and cross each other in 10.8 seconds.

### Step 2: Convert the speed of Train A from km/h to m/s
To work with meters and seconds, we need to convert the speed of Train A from kilometers per hour to meters per second.

\[ \text{Speed in m/s} = \text{Speed in km/h} \times \frac{1000 \text{ meters}}{3600 \text{ seconds}} = \text{Speed in km/h} \times \frac{5}{18} \]

For Train A:
\[ \text{Speed of Train A} = 60 \times \frac{5}{18} = \frac{300}{18} = 16.67 \text{ m/s} \]

### Step 3: Calculate the total distance covered when the trains cross each other
When two trains cross each other, the total distance covered is the sum of their lengths.

\[ \text{Total distance} = \text{Length of Train A} + \text{Length of Train B} = 180 \text{ m} + 270 \text{ m} = 450 \text{ m} \]

### Step 4: Use the formula for relative speed
When two objects move towards each other, their speeds add up. The relative speed (combined speed) of both trains is:

\[ \text{Relative speed} = \text{Speed of Train A} + \text{Speed of Train B} \]

Let the speed of Train B in m/s be \( v_B \).

\[ \text{Relative speed} = 16.67 + v_B \]

### Step 5: Use the time taken to cross each other
The time taken to cross each other is given as 10.8 seconds. We can use the formula:

\[ \text{Distance} = \text{Relative speed} \times \text{Time} \]

Substituting the known values:

\[ 450 = (16.67 + v_B) \times 10.8 \]

### Step 6: Solve for \( v_B \)
Now, we can solve for \( v_B \):

\[ 450 = 180.36 + 10.8v_B \]
\[ 450 - 180.36 = 10.8v_B \]
\[ 269.64 = 10.8v_B \]
\[ v_B = \frac{269.64}{10.8} \approx 24.94 \text{ m/s} \]

### Step 7: Convert \( v_B \) back to km/h
Now, we convert the speed of Train B back to km/h:

\[ \text{Speed in km/h} = v_B \times \frac{18}{5} \]
\[ \text{Speed of Train B} = 24.94 \times \frac{18}{5} \approx 89.784 \text{ km/h} \]

### Final Answer
The speed of the second train is approximately **89.78 km/h**.

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