A car travels half of the distance with constant velocity 40 km/h and another half with a constant velocity of 60 km/h along a straight line. The average velocity of the car is

Options

A. 24 km/h
B. 48 km/h
C. 60 km/h
D. 40 km/h

Answer

To find the average velocity of the car that travels half of the distance at a constant velocity of 40 km/h and the other half at 60 km/h, we can follow these steps:

### Step 1: Define the total distance
Let the total distance traveled by the car be \( D \). Therefore, half of the distance is \( \frac{D}{2} \).

### Step 2: Calculate the time taken for the first half of the distance
The car travels the first half of the distance \( \frac{D}{2} \) at a velocity of 40 km/h.
Using the formula for time:
\[ t_1 = \frac{\text{distance}}{\text{velocity}} = \frac{\frac{D}{2}}{40} = \frac{D}{80} \text{ hours} \]

### Step 3: Calculate the time taken for the second half of the distance
The car travels the second half of the distance \( \frac{D}{2} \) at a velocity of 60 km/h.
Using the same formula for time:
\[ t_2 = \frac{\text{distance}}{\text{velocity}} = \frac{\frac{D}{2}}{60} = \frac{D}{120} \text{ hours} \]

### Step 4: Calculate the total time taken
The total time taken \( T \) is the sum of the times for both halves:
\[ T = t_1 + t_2 = \frac{D}{80} + \frac{D}{120} \]
To add these fractions, we need a common denominator. The least common multiple of 80 and 120 is 240.
\[ T = \frac{3D}{240} + \frac{2D}{240} = \frac{5D}{240} = \frac{D}{48} \text{ hours} \]

### Step 5: Calculate the average velocity
The average velocity \( V_{avg} \) is defined as the total displacement divided by the total time taken:
\[ V_{avg} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{D}{T} = \frac{D}{\frac{D}{48}} = 48 \text{ km/h} \]

### Final Answer
The average velocity of the car is **48 km/h**.

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