Two trains of length 190 m and 210 m respectively, are running in opposite directions on parallel tracks. If their speeds are 40 km/hr and 32 km/hr respectively in what time will they cross each other?

Options

A. 20 seconds
B. 22 second
C. 25 second
D. 30 second

Answer

To solve the problem of two trains crossing each other, we can follow these steps:

### Step 1: Identify the lengths of the trains
- Train 1 length (L1) = 190 m
- Train 2 length (L2) = 210 m

### Step 2: Identify the speeds of the trains
- Speed of Train 1 (V1) = 40 km/hr
- Speed of Train 2 (V2) = 32 km/hr

### Step 3: Calculate the relative speed of the trains
Since the trains are moving in opposite directions, their speeds will be added to find the relative speed.
\[ \text{Relative Speed} = V1 + V2 = 40 \text{ km/hr} + 32 \text{ km/hr} = 72 \text{ km/hr} \]

### Step 4: Convert the relative speed from km/hr to m/s
To convert km/hr to m/s, we use the conversion factor \( \frac{5}{18} \).
\[ \text{Relative Speed in m/s} = 72 \text{ km/hr} \times \frac{5}{18} = 20 \text{ m/s} \]

### Step 5: Calculate the total length of the trains
The total length (L) of the two trains is the sum of their lengths.
\[ L = L1 + L2 = 190 \text{ m} + 210 \text{ m} = 400 \text{ m} \]

### Step 6: Calculate the time taken to cross each other
The time (T) taken to cross each other can be calculated using the formula:
\[ T = \frac{\text{Total Length}}{\text{Relative Speed}} \]
Substituting the values we have:
\[ T = \frac{400 \text{ m}}{20 \text{ m/s}} = 20 \text{ seconds} \]

### Conclusion
The two trains will cross each other in **20 seconds**.

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