The time taken by the faster train of length a metres running at x km/h to pass the slower train of length b metres running at y km/h in the same direction = The time taken to cover (a + b) metres in _______ km/h.

Answer

To solve the problem, we need to find the time taken by the faster train to pass the slower train and express that time in terms of the distance covered and the speed at which it is covered.

### Step-by-Step Solution:

1. **Identify the lengths of the trains and their speeds**:
- Let the length of the faster train be \( a \) meters.
- Let the length of the slower train be \( b \) meters.
- Let the speed of the faster train be \( x \) km/h.
- Let the speed of the slower train be \( y \) km/h.

2. **Calculate the total distance to be covered**:
- When the faster train passes the slower train, it needs to cover the length of both trains. Therefore, the total distance to be covered is:
\[ \text{Total Distance} = a + b \text{ meters} \]

3. **Convert the distance from meters to kilometers**:
- Since the speeds are given in km/h, we need to convert the distance from meters to kilometers:
\[ a + b \text{ meters} = \frac{a + b}{1000} \text{ kilometers} \]

4. **Determine the relative speed of the two trains**:
- Since both trains are moving in the same direction, the relative speed of the faster train with respect to the slower train is:
\[ \text{Relative Speed} = x - y \text{ km/h} \]

5. **Calculate the time taken to pass the slower train**:
- The time taken to pass the slower train can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
- Substituting the values we have:
\[ \text{Time} = \frac{\frac{a + b}{1000}}{x - y} \]

6. **Express the time in terms of the distance covered and speed**:
- The time taken to cover \( a + b \) meters in km/h is equivalent to the time taken to cover \( a + b \) meters at the relative speed of \( x - y \) km/h.

### Final Answer:
The time taken to cover \( a + b \) meters in \( (x - y) \) km/h.