Two trains are moving in the same direction at speeds of 54km/h and 92km/h, their lengths are 400m and 360m respectively. What is the time taken (in seconds) by faster train to cross the slower train?

Options

A. A)60
B. B)72
C. C)81
D. D)90

Answer

To solve the problem of how long it takes for the faster train to cross the slower train, we can follow these steps:

### Step 1: Determine the lengths of the trains
- The length of the first train (slower train) = 400 meters
- The length of the second train (faster train) = 360 meters

### Step 2: Calculate the total distance to be covered
- Total distance = Length of the slower train + Length of the faster train
- Total distance = 400 m + 360 m = 760 m

### Step 3: Determine the speeds of the trains
- Speed of the slower train = 54 km/h
- Speed of the faster train = 92 km/h

### Step 4: Calculate the relative speed
- Since both trains are moving in the same direction, the relative speed is the difference in their speeds.
- Relative speed = Speed of the faster train - Speed of the slower train
- Relative speed = 92 km/h - 54 km/h = 38 km/h

### Step 5: 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 = 38 km/h × (5/18) = (38 × 5) / 18 = 190 / 18 m/s
- Simplifying gives us approximately 10.56 m/s.

### Step 6: Calculate the time taken to cross the slower train
- Time = Distance / Speed
- Time = Total distance / Relative speed
- Time = 760 m / (190 / 18) m/s
- Time = 760 m × (18 / 190) s
- Time = (760 × 18) / 190 seconds

### Step 7: Simplify the calculation
- Time = 13680 / 190 seconds
- Time = 72 seconds

### Final Answer
The time taken by the faster train to cross the slower train is **72 seconds**.

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