Two trains, 80 metres and 120 metres long are running at the speed of 25km/hr and 35 km/hr respectively in the same direction on parallel tracks. How many seconds will they take to pass each other?

Options

A. A)48
B. B)64
C. C)70
D. D)72

Answer

To solve the problem of how long it will take for the two trains to pass each other, we can follow these steps:

### Step 1: Calculate the total distance to be covered
The total distance that needs to be covered when the two trains pass each other is the sum of their lengths.

- Length of Train 1 = 80 meters
- Length of Train 2 = 120 meters

**Total Distance = Length of Train 1 + Length of Train 2**
\[ \text{Total Distance} = 80 \, \text{meters} + 120 \, \text{meters} = 200 \, \text{meters} \]

### Step 2: Calculate the relative speed of the trains
Since both trains are moving in the same direction, the relative speed is the difference between their speeds.

- Speed of Train 1 = 25 km/hr
- Speed of Train 2 = 35 km/hr

**Relative Speed = Speed of Train 2 - Speed of Train 1**
\[ \text{Relative Speed} = 35 \, \text{km/hr} - 25 \, \text{km/hr} = 10 \, \text{km/hr} \]

### Step 3: Convert the relative speed from km/hr to m/s
To convert the speed from kilometers per hour to meters per second, we use the conversion factor \( \frac{5}{18} \).

**Relative Speed in m/s = Relative Speed in km/hr × \( \frac{5}{18} \)**
\[ \text{Relative Speed in m/s} = 10 \, \text{km/hr} \times \frac{5}{18} = \frac{50}{18} \approx 2.78 \, \text{m/s} \]

### Step 4: Calculate the time taken to pass each other
Time is calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the total distance and the relative speed:
\[ \text{Time} = \frac{200 \, \text{meters}}{2.78 \, \text{m/s}} \]

### Step 5: Perform the calculation
Calculating the time:
\[ \text{Time} \approx 72 \, \text{seconds} \]

### Final Answer
The two trains will take approximately **72 seconds** to pass each other.

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