A train .travelling at 100 kmph overtakes a motorbike travelling at 64 kmph in 40 seconds. What is the length of the train (in meters)?

Options

A. 1777
B. 1822
C. 400
D. 1111

Answer

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

### Step 1: Calculate the relative speed of the train with respect to the motorbike.
The speed of the train is 100 km/h and the speed of the motorbike is 64 km/h. Since they are moving in the same direction, we subtract the speed of the motorbike from the speed of the train.

\[ \text{Relative Speed} = \text{Speed of Train} - \text{Speed of Motorbike} = 100 \text{ km/h} - 64 \text{ km/h} = 36 \text{ km/h} \]

### Step 2: Convert the relative speed from km/h to m/s.
To convert km/h to m/s, we multiply by \(\frac{5}{18}\).

\[ \text{Relative Speed in m/s} = 36 \text{ km/h} \times \frac{5}{18} = 10 \text{ m/s} \]

### Step 3: Use the formula for distance to find the length of the train.
The distance (length of the train) can be calculated using the formula:

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

Here, the time taken to overtake is given as 40 seconds.

\[ \text{Length of Train} = \text{Relative Speed} \times \text{Time} = 10 \text{ m/s} \times 40 \text{ s} = 400 \text{ meters} \]

### Conclusion:
The length of the train is **400 meters**.

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