A man goes to a place at the rate of 4kmph he comes back on a bicycle at 16 kmph his average speed for the entire journey is

Options

A. 5km/hr
B. 6.4km/hr
C. 8.5km/hr
D. 10 km/hr

Answer

To find the average speed for the entire journey, we can use the formula for average speed when the distances are the same:

**Average Speed = (2 * S1 * S2) / (S1 + S2)**

Where:
- S1 = speed going to the place
- S2 = speed coming back

### Step-by-Step Solution:

1. **Identify the Speeds**:
- Speed going to the place (S1) = 4 km/h
- Speed coming back (S2) = 16 km/h

2. **Apply the Average Speed Formula**:
- Substitute the values into the formula:
\[ \text{Average Speed} = \frac{2 \times S1 \times S2}{S1 + S2} \]
\[ \text{Average Speed} = \frac{2 \times 4 \times 16}{4 + 16} \]

3. **Calculate the Denominator**:
- Calculate \( S1 + S2 \):
\[ 4 + 16 = 20 \]

4. **Calculate the Numerator**:
- Calculate \( 2 \times 4 \times 16 \):
\[ 2 \times 4 = 8 \]
\[ 8 \times 16 = 128 \]

5. **Combine the Results**:
- Now substitute back into the average speed formula:
\[ \text{Average Speed} = \frac{128}{20} \]

6. **Simplify the Fraction**:
- Divide 128 by 20:
\[ \text{Average Speed} = 6.4 \text{ km/h} \]

### Final Answer:
The average speed for the entire journey is **6.4 km/h**.

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