Two trains are moving in the same direction at the speeds of 35km/hr and 71 km/hr. The time taken by faster train to cross a man sitting in the slower train is 48 seconds. What will be the length (in metres) of the faster train?

Options

A. A)540
B. B)420
C. C)480
D. D)660

Answer

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

### Step 1: Determine the speeds of the trains
- The speed of the slower train = 35 km/hr
- The speed of the faster train = 71 km/hr

### Step 2: Calculate the relative speed
Since both trains are moving in the same direction, the relative speed is the difference between their speeds:
\[ \text{Relative Speed} = \text{Speed of Faster Train} - \text{Speed of Slower Train} \]
\[ \text{Relative Speed} = 71 \text{ km/hr} - 35 \text{ km/hr} = 36 \text{ km/hr} \]

### Step 3: Convert the relative speed from km/hr to m/s
To convert km/hr to m/s, we use the conversion factor \( \frac{5}{18} \):
\[ \text{Relative Speed in m/s} = 36 \text{ km/hr} \times \frac{5}{18} = 10 \text{ m/s} \]

### Step 4: Use the time taken to cross the man
The time taken by the faster train to cross a man sitting in the slower train is given as 48 seconds.

### Step 5: Calculate the length of the faster train
The length of the faster train can be calculated using the formula:
\[ \text{Length} = \text{Speed} \times \text{Time} \]
Substituting the values we have:
\[ \text{Length} = 10 \text{ m/s} \times 48 \text{ seconds} = 480 \text{ meters} \]

### Conclusion
The length of the faster train is **480 meters**.

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