Two trains travel in the same direction at the speed of 56km/h and 29km/h respectively. The faster train passes a man in the slower train in 10 seconds. The length of the faster train (in metres) is

Options

A. A)100
B. B)80
C. C)75
D. D)120

Answer

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

### Step 1: Determine the speeds of the trains
The speeds of the two trains are given as:
- Speed of the faster train = 56 km/h
- Speed of the slower train = 29 km/h

### Step 2: Calculate the relative speed
Since both trains are moving in the same direction, the relative speed is the difference between their speeds:
\[ \text{Relative Speed} = \text{Speed of Faster Train} - \text{Speed of Slower Train} = 56 \text{ km/h} - 29 \text{ km/h} = 27 \text{ km/h} \]

### Step 3: Convert the relative speed from km/h to m/s
To convert km/h to m/s, we use the conversion factor \( \frac{5}{18} \):
\[ \text{Relative Speed in m/s} = 27 \text{ km/h} \times \frac{5}{18} = 7.5 \text{ m/s} \]

### Step 4: Use the time taken to pass the man
The problem states that the faster train passes a man in the slower train in 10 seconds. This time is given as:
\[ t = 10 \text{ seconds} \]

### Step 5: Calculate the length of the faster train
The length of the faster train can be calculated using the formula:
\[ \text{Length} = \text{Relative Speed} \times \text{Time} \]
Substituting the values we have:
\[ \text{Length} = 7.5 \text{ m/s} \times 10 \text{ s} = 75 \text{ m} \]

### Conclusion
The length of the faster train is **75 meters**.

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