A person goes from one point to another point with a speed of 5km/h and comes back to starting point with a speed of 3 km/h. Find the average speed for the whole journey.

Options

A. 4.5 km/h
B. 4 km/h
C. 4.25 km/h
D. 3.75 km/h

Answer

To find the average speed for the whole journey, we can use the formula for average speed when the distances are the same but the speeds are different. The formula is:

\[ \text{Average Speed} = \frac{2 \cdot S_1 \cdot S_2}{S_1 + S_2} \]

where \( S_1 \) is the speed for the first part of the journey and \( S_2 \) is the speed for the return journey.

### Step-by-Step Solution:

1. **Identify the Speeds**:
- Speed from A to B, \( S_1 = 5 \) km/h
- Speed from B to A, \( S_2 = 3 \) km/h

2. **Apply the Average Speed Formula**:
- Substitute the values into the formula:
\[ \text{Average Speed} = \frac{2 \cdot 5 \cdot 3}{5 + 3} \]

3. **Calculate the Denominator**:
- \( S_1 + S_2 = 5 + 3 = 8 \)

4. **Calculate the Numerator**:
- \( 2 \cdot 5 \cdot 3 = 30 \)

5. **Combine the Results**:
- Now substitute back into the formula:
\[ \text{Average Speed} = \frac{30}{8} \]

6. **Simplify the Fraction**:
- \( \frac{30}{8} = 3.75 \) km/h

### Final Answer:
The average speed for the whole journey is **3.75 km/h**.

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