A man makes his upward journey at 16 km/h and downward journey at 28 km/h. What is his average speed ?

Options

A. 32 km/h
B. 56 km/h
C. 20.36 km/h
D. 22 km/h

Answer

To find the average speed of a man making an upward journey at 16 km/h and a downward journey at 28 km/h, we can use the formula for average speed when the distance is the same for both journeys. The formula is:

\[ \text{Average Speed} = \frac{2xy}{x + y} \]

where \(x\) is the speed during the upward journey and \(y\) is the speed during the downward journey.

### Step-by-Step Solution:

1. **Identify the Speeds**:
- Upward speed (\(x\)) = 16 km/h
- Downward speed (\(y\)) = 28 km/h

2. **Substitute the Values into the Formula**:
\[ \text{Average Speed} = \frac{2 \times 16 \times 28}{16 + 28} \]

3. **Calculate the Denominator**:
\[ 16 + 28 = 44 \]

4. **Calculate the Numerator**:
\[ 2 \times 16 \times 28 = 2 \times 448 = 896 \]

5. **Divide the Numerator by the Denominator**:
\[ \text{Average Speed} = \frac{896}{44} \]

6. **Perform the Division**:
\[ \frac{896}{44} = 20.36 \text{ km/h} \]

Thus, the average speed of the man for the entire journey is **20.36 km/h**.