A motorist travels from A to B at a speed of `40 km//hr` and returns at a speed of 60 km/hr. His average speed will be:

Options

A. `40 km//hr`
B. `48 km//hr`
C. `50 km//hr`
D. `60 km//hr`

Explanation

To find the average speed of the motorist who travels from point A to point B and back, we can follow these steps:

### Step 1: Define the Variables
Let the distance from A to B be \( D \) kilometers. The speed from A to B is \( 40 \) km/h, and the speed from B to A is \( 60 \) km/h.

### Step 2: Calculate the Time Taken for Each Leg of the Journey
- **Time taken to travel from A to B (T1)**:
\[ T_1 = \frac{D}{40} \text{ hours} \]

- **Time taken to travel from B to A (T2)**:
\[ T_2 = \frac{D}{60} \text{ hours} \]

### Step 3: Calculate the Total Distance and Total Time
- **Total Distance (D_total)**:
\[ D_{total} = D + D = 2D \text{ kilometers} \]

- **Total Time (T_total)**:
\[ T_{total} = T_1 + T_2 = \frac{D}{40} + \frac{D}{60} \]

### Step 4: Find a Common Denominator for Total Time
To add the fractions, we find a common denominator, which is \( 120 \):
\[ T_{total} = \frac{D \times 3}{120} + \frac{D \times 2}{120} = \frac{5D}{120} = \frac{D}{24} \text{ hours} \]

### Step 5: Calculate the Average Speed
The average speed \( V_{avg} \) is given by the formula:
\[ V_{avg} = \frac{D_{total}}{T_{total}} = \frac{2D}{\frac{D}{24}} = 2D \times \frac{24}{D} = 48 \text{ km/h} \]

### Conclusion
The average speed of the motorist for the entire journey is \( 48 \) km/h.

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