A man covers half of his journey at 6km/hr and the remaining half at 3km/hr. His average speed is

Options

A. 9 km/hr
B. 4.5 km/hr
C. 4 km/hr
D. 3 km/hr

Answer

To find the average speed of the man covering his journey, we can follow these steps:

### Step 1: Define the total distance
Let the total distance of the journey be \( X \) kilometers.

**Hint:** Start by defining the total distance to simplify calculations.

### Step 2: Calculate the distance for each half of the journey
Since the man covers half of his journey at 6 km/hr and the other half at 3 km/hr, each half of the journey is \( \frac{X}{2} \) kilometers.

**Hint:** Remember that half of the total distance is \( \frac{X}{2} \).

### Step 3: Calculate the time taken for the first half of the journey
The time taken to cover the first half of the journey at 6 km/hr is given by:
\[ \text{Time}_1 = \frac{\text{Distance}}{\text{Speed}} = \frac{\frac{X}{2}}{6} = \frac{X}{12} \text{ hours} \]

**Hint:** Use the formula for time, which is distance divided by speed.

### Step 4: Calculate the time taken for the second half of the journey
The time taken to cover the second half of the journey at 3 km/hr is given by:
\[ \text{Time}_2 = \frac{\frac{X}{2}}{3} = \frac{X}{6} \text{ hours} \]

**Hint:** Again, apply the time formula for the second half of the journey.

### Step 5: Calculate the total time for the journey
The total time taken for the entire journey is the sum of the time for both halves:
\[ \text{Total Time} = \text{Time}_1 + \text{Time}_2 = \frac{X}{12} + \frac{X}{6} \]

To add these fractions, find a common denominator (which is 12):
\[ \text{Total Time} = \frac{X}{12} + \frac{2X}{12} = \frac{3X}{12} = \frac{X}{4} \text{ hours} \]

**Hint:** When adding fractions, ensure they have a common denominator.

### Step 6: Calculate the average speed
The average speed is calculated using the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{X}{\frac{X}{4}} = 4 \text{ km/hr} \]

**Hint:** Average speed is total distance divided by total time.

### Final Answer
The average speed of the man is **4 km/hr**.