Two trains are running in opposite directions on parallel tracks at the speeds of 42 km hi and 57 kmh, respectively. They take 18 seconds to cross each other. If the length of one train is 295 m, then the length (in m) of the other train is:

Options

A. 245
B. 200
C. 300
D. 225

Answer

To find the length of the other train, we can follow these steps:

### Step 1: Convert the speeds from km/h to m/s
To convert km/h to m/s, we use the conversion factor:
1 km/h = (1000 m / 3600 s) = 5/18 m/s.

- Speed of the first train = 42 km/h = 42 * (5/18) m/s = 11.67 m/s.
- Speed of the second train = 57 km/h = 57 * (5/18) m/s = 15.83 m/s.

### Step 2: Calculate the relative speed of the two trains
Since the trains are moving in opposite directions, we add their speeds to find the relative speed.

Relative speed = Speed of Train 1 + Speed of Train 2
= 11.67 m/s + 15.83 m/s = 27.5 m/s.

### Step 3: Calculate the total distance covered when they cross each other
The total distance covered when the two trains cross each other is equal to the sum of their lengths.

Let the length of the second train be x meters. The length of the first train is given as 295 meters.

Total distance = Length of Train 1 + Length of Train 2
= 295 m + x m.

### Step 4: Use the time taken to cross each other to find the total distance
The time taken to cross each other is given as 18 seconds.

Using the formula:
Distance = Speed × Time,
we can find the total distance:

Total distance = Relative speed × Time
= 27.5 m/s × 18 s = 495 m.

### Step 5: Set up the equation and solve for x
Now we can set up the equation using the total distance:

295 m + x m = 495 m.

Subtract 295 m from both sides:

x = 495 m - 295 m,
x = 200 m.

### Conclusion
The length of the other train is 200 meters.

---