A train travels a distance between two stations, X km apart, at a speed of 60 km per hour for the onward journey and 90 km per hour on the retum journey. What is the average speed of the train?
A)`77 km//hr`
B)`76 km//hr`
C)`75 km//hr`
D)`72 km//hr`

Options

A. `77 km//hr`
B. `76 km//hr`
C. `75 km//hr`
D. `72 km//hr`

Answer

To find the average speed of the train for the entire journey, we can use the formula for average speed when two different speeds are involved:

**Average Speed = (2 * Speed1 * Speed2) / (Speed1 + Speed2)**

Where:
- Speed1 = 60 km/h (onward journey)
- Speed2 = 90 km/h (return journey)

### Step-by-Step Solution:

1. **Identify the speeds**:
- Onward journey speed (Speed1) = 60 km/h
- Return journey speed (Speed2) = 90 km/h

2. **Apply the average speed formula**:
\[ \text{Average Speed} = \frac{2 \times \text{Speed1} \times \text{Speed2}}{\text{Speed1} + \text{Speed2}} \]

3. **Substitute the values into the formula**:
\[ \text{Average Speed} = \frac{2 \times 60 \times 90}{60 + 90} \]

4. **Calculate the denominator**:
\[ \text{Speed1} + \text{Speed2} = 60 + 90 = 150 \]

5. **Calculate the numerator**:
\[ 2 \times 60 \times 90 = 10800 \]

6. **Now divide the numerator by the denominator**:
\[ \text{Average Speed} = \frac{10800}{150} \]

7. **Perform the division**:
\[ \text{Average Speed} = 72 \text{ km/h} \]

### Conclusion:
The average speed of the train for the entire journey is **72 km/h**.

### Answer:
**Option D: 72 km/h**

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