Two trains are moving in the opposite directions at speeds of 43 km/h and 51 km/h respectively. The time taken by the slower train to cross a man sitting in the faster train is 9 seconds. What is the length (in metre) of the slower train?

Options

A. 235
B. 338.4
C. 470
D. 940

Answer

To solve the problem step by step, we need to find the length of the slower train based on the information provided.

### Step 1: Understand the problem
We have two trains moving in opposite directions. The speeds of the trains are:
- Speed of the slower train = 43 km/h
- Speed of the faster train = 51 km/h

The time taken by the slower train to cross a man sitting in the faster train is 9 seconds.

### Step 2: Calculate the relative speed
When two objects move in opposite directions, their speeds add up. Therefore, the relative speed (V_rel) of the two trains is:
\[ V_{\text{rel}} = V_{\text{slower}} + V_{\text{faster}} = 43 \text{ km/h} + 51 \text{ km/h} = 94 \text{ km/h} \]

### Step 3: Convert the relative speed to meters per second
To convert km/h to m/s, we use the conversion factor \( \frac{5}{18} \):
\[ V_{\text{rel}} = 94 \text{ km/h} \times \frac{5}{18} = \frac{470}{18} \approx 26.11 \text{ m/s} \]

### Step 4: Use the formula for distance
The distance covered by the slower train while crossing the man is equal to the length of the slower train (L). The formula relating distance, speed, and time is:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Thus, the length of the slower train can be calculated as:
\[ L = V_{\text{rel}} \times \text{Time} = 26.11 \text{ m/s} \times 9 \text{ s} \]

### Step 5: Calculate the length of the slower train
Now, we calculate the length:
\[ L = 26.11 \text{ m/s} \times 9 \text{ s} = 235 \text{ m} \]

### Final Answer
The length of the slower train is **235 meters**.

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