A vehicle travels half the distance (L) with speed ` V_1` and the other half with speed ` V_2`, then its average speed is .

Options

A. a. `v_1 + v_2/2`
B. b. `2v_1 + v_2/v_1 + v_2`
C. c. `2v_(1)v_2/(v_1 + v_2)`
D. d. `(v_1 + v_2)/v_(1)v_(2)`

Explanation

To find the average speed of a vehicle that travels half the distance \( L \) with speed \( V_1 \) and the other half with speed \( V_2 \), we can follow these steps:

### Step 1: Define the total distance
The total distance \( D \) traveled by the vehicle is:
\[ D = L + L = 2L \]

### Step 2: Calculate the time for the first half of the distance
The time taken to travel the first half of the distance \( L \) at speed \( V_1 \) is given by:
\[ t_1 = \frac{L}{V_1} \]

### Step 3: Calculate the time for the second half of the distance
The time taken to travel the second half of the distance \( L \) at speed \( V_2 \) is given by:
\[ t_2 = \frac{L}{V_2} \]

### Step 4: Calculate the total time taken
The total time \( T \) taken for the entire journey is the sum of the times for each half:
\[ T = t_1 + t_2 = \frac{L}{V_1} + \frac{L}{V_2} \]

### Step 5: Simplify the total time
We can factor out \( L \) from the total time:
\[ T = L \left( \frac{1}{V_1} + \frac{1}{V_2} \right) \]

### Step 6: Calculate the average speed
The average speed \( V_{avg} \) is defined as the total distance divided by the total time:
\[ V_{avg} = \frac{D}{T} = \frac{2L}{L \left( \frac{1}{V_1} + \frac{1}{V_2} \right)} \]
This simplifies to:
\[ V_{avg} = \frac{2}{\left( \frac{1}{V_1} + \frac{1}{V_2} \right)} \]

### Step 7: Further simplify the average speed expression
Using the formula for the sum of reciprocals, we can rewrite the average speed:
\[ V_{avg} = \frac{2 V_1 V_2}{V_1 + V_2} \]

### Conclusion
Thus, the average speed of the vehicle is:
\[ V_{avg} = \frac{2 V_1 V_2}{V_1 + V_2} \]