Two trains of lengths 50 m and 65 m are moving in the same direction at 18 m/s and 17 m/s, respect- ively. Find the time taken by the faster train to cross the slower train.

Options

A. a. 100s
B. b. 114s
C. c. 95s
D. d. 115s

Answer

To solve the problem of finding the time taken by the faster train to cross the slower train, we can follow these steps:

### Step 1: Identify the lengths of the trains
- Length of the first train (Train A) = 50 m
- Length of the second train (Train B) = 65 m

### Step 2: Identify the speeds of the trains
- Speed of Train A = 18 m/s
- Speed of Train B = 17 m/s

### Step 3: Calculate the total distance to be covered
When the faster train crosses the slower train, it needs to cover the combined lengths of both trains:
- Total distance = Length of Train A + Length of Train B
- Total distance = 50 m + 65 m = 115 m

### Step 4: Calculate the relative speed
Since both trains are moving in the same direction, the relative speed is the difference between their speeds:
- Relative speed = Speed of Train A - Speed of Train B
- Relative speed = 18 m/s - 17 m/s = 1 m/s

### Step 5: Calculate the time taken to cross
Using the formula for time:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
We can substitute the values we found:
- Time = Total distance / Relative speed
- Time = 115 m / 1 m/s = 115 seconds

### Final Answer
The time taken by the faster train to cross the slower train is **115 seconds**.

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