Two trains are moving in the opposite directions on parallel tracks at the speeds of 63 km/hr and 94.50 km/hr respectively. The first train passes a pole in 6 seconds whereas the second train passes a pole in 4 seconds. Find the time taken by the trains to cross each other completely?

Options

A. A) 4.80 sec.
B. B) 4.40 sec
C. C) 3.80 sec.
D. D) Can't be determined

Answer

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

### Step 1: Determine the lengths of the trains
To find the lengths of the trains, we can use the formula:
\[ \text{Length of Train} = \text{Speed} \times \text{Time} \]

For Train 1 (speed = 63 km/hr, time = 6 seconds):
1. Convert the speed from km/hr to m/s:
\[ 63 \text{ km/hr} = \frac{63 \times 1000}{3600} = 17.5 \text{ m/s} \]
2. Calculate the length of Train 1:
\[ L_1 = 17.5 \text{ m/s} \times 6 \text{ s} = 105 \text{ m} \]

For Train 2 (speed = 94.5 km/hr, time = 4 seconds):
1. Convert the speed from km/hr to m/s:
\[ 94.5 \text{ km/hr} = \frac{94.5 \times 1000}{3600} = 26.25 \text{ m/s} \]
2. Calculate the length of Train 2:
\[ L_2 = 26.25 \text{ m/s} \times 4 \text{ s} = 105 \text{ m} \]

### Step 2: Calculate the relative speed of the trains
Since the trains are moving in opposite directions, we can add their speeds to find the relative speed:
\[ \text{Relative Speed} = 17.5 \text{ m/s} + 26.25 \text{ m/s} = 43.75 \text{ m/s} \]

### Step 3: Calculate the total length to be crossed
The total length when the two trains cross each other is the sum of the lengths of both trains:
\[ \text{Total Length} = L_1 + L_2 = 105 \text{ m} + 105 \text{ m} = 210 \text{ m} \]

### Step 4: Calculate the time taken to cross each other
Using the formula:
\[ \text{Time} = \frac{\text{Total Length}}{\text{Relative Speed}} \]
Substituting the values:
\[ \text{Time} = \frac{210 \text{ m}}{43.75 \text{ m/s}} \approx 4.8 \text{ seconds} \]

### Final Answer
The time taken by the trains to cross each other completely is approximately **4.8 seconds**.

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