A bo walks to his school at a distance of 6 km with constant speed of `2.5 kmh^(-1)` and walks back with a constant speed of `4 kmh^(-1)`. His average speed for round trip expressed in `kmh^(-1)`, is

Options

A. 24/13
B. 40/13
C. 3
D. `1//2`

Explanation

To find the average speed for the round trip, we can follow these steps:

### Step 1: Calculate the total distance
The boy walks to school and back, so the total distance \( D \) is:
\[ D = 6 \text{ km (to school)} + 6 \text{ km (back)} = 12 \text{ km} \]

### Step 2: Calculate the time taken for each leg of the trip
1. **Time taken to walk to school**:
- Distance = 6 km
- Speed = 2.5 km/h
\[ \text{Time}_1 = \frac{\text{Distance}}{\text{Speed}} = \frac{6 \text{ km}}{2.5 \text{ km/h}} = 2.4 \text{ hours} \]

2. **Time taken to walk back home**:
- Distance = 6 km
- Speed = 4 km/h
\[ \text{Time}_2 = \frac{\text{Distance}}{\text{Speed}} = \frac{6 \text{ km}}{4 \text{ km/h}} = 1.5 \text{ hours} \]

### Step 3: Calculate the total time for the round trip
\[ \text{Total Time} = \text{Time}_1 + \text{Time}_2 = 2.4 \text{ hours} + 1.5 \text{ hours} = 3.9 \text{ hours} \]

### Step 4: Calculate the average speed
Average speed \( V_{\text{avg}} \) is given by the formula:
\[ V_{\text{avg}} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{12 \text{ km}}{3.9 \text{ hours}} \approx 3.08 \text{ km/h} \]

### Final Result
Thus, the average speed for the round trip is approximately:
\[ V_{\text{avg}} \approx 3.08 \text{ km/h} \]