The time taken by a train l metres long running at x km/h to pass a man who is running at y km/h in the direction opposite to that of the train = The time taken to cover l metres at _______ km/h.

Answer

To solve the problem, we need to determine the effective speed at which the train passes the man running in the opposite direction. Here’s the step-by-step solution:

### Step 1: Understand the scenario
- We have a train that is **L meters long**.
- The train is moving at a speed of **x km/h**.
- A man is running at a speed of **y km/h** in the opposite direction.

### Step 2: Calculate the relative speed
- Since the man is running in the opposite direction to the train, we need to add the speeds of both the train and the man to find the relative speed.
- The relative speed of the train with respect to the man is given by:
\[ \text{Relative Speed} = x + y \text{ km/h} \]

### Step 3: Convert the relative speed to meters per second
- To find the time taken to pass the man, we need to convert the relative speed from km/h to m/s.
- We know that:
\[ 1 \text{ km/h} = \frac{1000 \text{ meters}}{3600 \text{ seconds}} = \frac{5}{18} \text{ m/s} \]
- Therefore, the relative speed in m/s is:
\[ \text{Relative Speed in m/s} = (x + y) \times \frac{5}{18} \]

### Step 4: Calculate the time taken to pass the man
- The time taken to pass the man is calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
- Here, the distance is the length of the train **L meters**, and the speed is the relative speed in m/s.
- Thus, the time taken to pass the man is:
\[ \text{Time} = \frac{L}{(x + y) \times \frac{5}{18}} \]

### Step 5: Simplify the expression
- Rearranging the formula gives:
\[ \text{Time} = \frac{L \times 18}{(x + y) \times 5} \]

### Conclusion
- The time taken by the train to pass the man is equal to the time taken to cover **L meters at a speed of \(x + y\) km/h**.