A covered half of his journey at 20 km/h and rest at 60 km/h. What is the average speed of the man?

Options

A. 30
B. 32
C. 36
D. 40

Answer

To find the average speed of a man who covers half of his journey at 20 km/h and the other half at 60 km/h, we can follow these steps:

### Step-by-Step Solution:

1. **Assume Total Distance**:
Let's assume the total distance of the journey is \(2d\) kilometers. This means half of the journey is \(d\) kilometers.

**Hint**: Choose a simple total distance to make calculations easier.

2. **Calculate Time for Each Half**:
- For the first half of the journey (distance \(d\) at 20 km/h):
\[ \text{Time}_1 = \frac{d}{20} \]
- For the second half of the journey (distance \(d\) at 60 km/h):
\[ \text{Time}_2 = \frac{d}{60} \]

**Hint**: Remember that time is calculated as distance divided by speed.

3. **Calculate Total Time**:
The total time taken for the journey is the sum of the time for each half:
\[ \text{Total Time} = \text{Time}_1 + \text{Time}_2 = \frac{d}{20} + \frac{d}{60} \]

**Hint**: When adding fractions, find a common denominator.

4. **Finding a Common Denominator**:
The least common multiple of 20 and 60 is 60. We can rewrite the times:
\[ \frac{d}{20} = \frac{3d}{60}, \quad \text{and} \quad \frac{d}{60} = \frac{d}{60} \]
Therefore,
\[ \text{Total Time} = \frac{3d}{60} + \frac{d}{60} = \frac{4d}{60} = \frac{d}{15} \]

**Hint**: Simplifying fractions can help in finding the total time more easily.

5. **Calculate Average Speed**:
The average speed is given by the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{2d}{\frac{d}{15}} = 2d \times \frac{15}{d} = 30 \text{ km/h} \]

**Hint**: The average speed is the total distance divided by the total time.

### Final Answer:
The average speed of the man is **30 km/h**.