A 248-m-long train travelling at 88 km`//`h takes 30 seconds to cross another train, `x` m long, travelling at 34 km/h in the same direction. What is the value of `x` ?

Options

A. 192
B. 197
C. 202
D. 207

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the problem
We have two trains:
- Train A (length = 248 m, speed = 88 km/h)
- Train B (length = x m, speed = 34 km/h)

Train A takes 30 seconds to completely cross Train B while both are moving in the same direction.

### Step 2: Calculate the relative speed
Since both trains are moving in the same direction, the relative speed is calculated by subtracting the speed of Train B from the speed of Train A.

\[ \text{Relative speed} = \text{Speed of Train A} - \text{Speed of Train B} = 88 \text{ km/h} - 34 \text{ km/h} = 54 \text{ km/h} \]

### Step 3: Convert the relative speed to meters per second
To convert km/h to m/s, we use the conversion factor \( \frac{5}{18} \).

\[ \text{Relative speed in m/s} = 54 \times \frac{5}{18} = 15 \text{ m/s} \]

### Step 4: Use the formula for distance
The total distance covered when Train A crosses Train B is the sum of their lengths, which is \( 248 + x \) meters. The formula relating speed, distance, and time is:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

Rearranging gives us:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

### Step 5: Substitute known values
We know the speed (15 m/s) and the time (30 seconds), so we can substitute these values into the equation:

\[ 248 + x = 15 \times 30 \]

### Step 6: Calculate the right side
Calculating \( 15 \times 30 \):

\[ 15 \times 30 = 450 \]

### Step 7: Set up the equation
Now we have:

\[ 248 + x = 450 \]

### Step 8: Solve for x
To find \( x \), we subtract 248 from both sides:

\[ x = 450 - 248 \]

Calculating the subtraction gives:

\[ x = 202 \]

### Final Answer
The length of Train B (x) is **202 meters**.

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