The distance between two stations A and B is 138 km. A train starts from A towards B and another from B to A at the same time and they meet after 6 h. The train travelling from A to B is slower by 7 km/h compared to other train from B to A, then find the speed of the slower train?

Answer

To solve the problem, we need to find the speed of the slower train that travels from station A to station B. Let's break down the solution step by step.

### Step 1: Define Variables
Let the speed of the train from B to A be \( S \) km/h.
Then, the speed of the train from A to B will be \( S - 7 \) km/h (since it is slower by 7 km/h).

### Step 2: Determine the Time of Travel
Both trains meet after 6 hours of travel. Therefore, the time taken by both trains is 6 hours.

### Step 3: Calculate the Distance Covered by Each Train
The distance covered by the train from A to B in 6 hours is:
\[ \text{Distance} = \text{Speed} \times \text{Time} = (S - 7) \times 6 \]

The distance covered by the train from B to A in 6 hours is:
\[ \text{Distance} = \text{Speed} \times \text{Time} = S \times 6 \]

### Step 4: Set Up the Equation
The total distance between the two stations A and B is 138 km. Therefore, we can set up the equation:
\[ (S - 7) \times 6 + S \times 6 = 138 \]

### Step 5: Simplify the Equation
Expanding the equation gives:
\[ 6(S - 7) + 6S = 138 \]
\[ 6S - 42 + 6S = 138 \]
\[ 12S - 42 = 138 \]

### Step 6: Solve for S
Now, add 42 to both sides:
\[ 12S = 138 + 42 \]
\[ 12S = 180 \]
Now, divide by 12:
\[ S = \frac{180}{12} = 15 \text{ km/h} \]

### Step 7: Find the Speed of the Slower Train
Now, we can find the speed of the slower train:
\[ \text{Speed of the slower train} = S - 7 = 15 - 7 = 8 \text{ km/h} \]

### Final Answer
The speed of the slower train is **8 km/h**.

---