A goods train of 50m. long is moving with speed 54 km/h. A man is sitting in a passanger train which is moving with 18 km/hr. with same direction. In how many second the goods train crosses the man sitting in a passanger train ?

Answer

To solve the problem of how long it takes for the goods train to cross the man sitting in the passenger train, we can follow these steps:

### Step 1: Identify the lengths and speeds
- Length of the goods train = 50 meters
- Speed of the goods train = 54 km/h
- Speed of the passenger train = 18 km/h

### Step 2: Calculate the relative speed
Since both trains are moving in the same direction, we need to find the relative speed of the goods train with respect to the passenger train.

Relative speed = Speed of goods train - Speed of passenger train

Relative speed = 54 km/h - 18 km/h = 36 km/h

### Step 3: Convert the relative speed from km/h to m/s
To convert km/h to m/s, we use the conversion factor (1 km/h = 5/18 m/s).

Relative speed in m/s = 36 km/h × (5/18)

Calculating this gives:
Relative speed in m/s = 36 × (5/18) = 10 m/s

### Step 4: Calculate the time taken to cross the man
The time taken to cross the man is given by the formula:

Time = Distance / Speed

Here, the distance to be covered is the length of the goods train (50 meters), and the speed is the relative speed we calculated (10 m/s).

Time = 50 m / 10 m/s = 5 seconds

### Final Answer
The goods train will take 5 seconds to cross the man sitting in the passenger train.

---