Two trains A and B start running together from the same point in the same direction at 40 kmph and 64 kmph respectively. If the length of each train is 300 m, then how long will it take for the train B to cross train A?

Options

A. 2 min 30 sec
B. 1 min 45 sec
C. 2 min 12 sec
D. 1 min 30 sec

Answer

To solve the problem of how long it will take for train B to cross train A, we can follow these steps:

### Step 1: Determine the speeds of the trains
Train A is moving at a speed of 40 km/h and Train B is moving at a speed of 64 km/h.

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

\[ \text{Relative Speed} = \text{Speed of B} - \text{Speed of A} = 64 \text{ km/h} - 40 \text{ km/h} = 24 \text{ km/h} \]

### Step 3: Convert the relative speed from km/h to m/s
To convert km/h to m/s, we multiply the speed by \(\frac{5}{18}\).

\[ \text{Relative Speed in m/s} = 24 \text{ km/h} \times \frac{5}{18} = \frac{120}{18} = \frac{20}{3} \text{ m/s} \]

### Step 4: Calculate the total distance to be covered
To cross Train A, Train B needs to cover the length of both trains. Given that each train is 300 m long, the total distance is:

\[ \text{Total Distance} = 300 \text{ m} + 300 \text{ m} = 600 \text{ m} \]

### Step 5: Use the formula for time
The time taken to cross Train A can be calculated using the formula:

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

Substituting the values we have:

\[ \text{Time} = \frac{600 \text{ m}}{\frac{20}{3} \text{ m/s}} = 600 \times \frac{3}{20} = 90 \text{ seconds} \]

### Conclusion
Thus, it will take Train B 90 seconds to completely cross Train A.