Two trains A and B start running together from the same point in the same direction at 90 kmph and 60 kmph respectively. If the length of each train is 250 m, then how long will it take for the train A to cross train B?

Options

A. 2 mins 15 secs
B. 1 min
C. 2 mins 05 secs
D. 1 min 30 secs

Answer

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

### Step 1: Determine the speeds of the trains
- Speed of train A = 90 km/h
- Speed of train B = 60 km/h

### Step 2: Calculate the relative speed of train A with respect to train B
Since both trains are moving in the same direction, the relative speed is calculated by subtracting the speed of train B from the speed of train A:
\[ \text{Relative Speed} = \text{Speed of A} - \text{Speed of B} = 90 \text{ km/h} - 60 \text{ km/h} = 30 \text{ km/h} \]

### Step 3: Calculate the total length to be crossed
Each train has a length of 250 m, so the total length that train A needs to cross train B is:
\[ \text{Total Length} = \text{Length of A} + \text{Length of B} = 250 \text{ m} + 250 \text{ m} = 500 \text{ m} \]

### Step 4: Convert the relative speed from km/h to m/s
To convert the relative speed from kilometers per hour to meters per second, we use the conversion factor:
\[ 1 \text{ km/h} = \frac{1000 \text{ m}}{3600 \text{ s}} = \frac{5}{18} \text{ m/s} \]
Thus,
\[ \text{Relative Speed in m/s} = 30 \text{ km/h} \times \frac{5}{18} = \frac{150}{18} \text{ m/s} = \frac{25}{3} \text{ m/s} \]

### Step 5: Calculate the time taken to cross
Using the formula:
\[ \text{Time} = \frac{\text{Total Length}}{\text{Relative Speed}} \]
Substituting the values we have:
\[ \text{Time} = \frac{500 \text{ m}}{\frac{25}{3} \text{ m/s}} = 500 \text{ m} \times \frac{3}{25} = 60 \text{ s} \]

### Step 6: Convert time from seconds to minutes
To convert seconds into minutes:
\[ \text{Time in minutes} = \frac{60 \text{ s}}{60} = 1 \text{ minute} \]

### Final Answer
Thus, the time taken for train A to cross train B is **1 minute**.

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