A car travels along a straight line for first half time with speed `40 km//h` and the second half time with speed `60 km//h`. Find the average speed of the car.

Options

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

Answer

To find the average speed of the car, we can follow these steps:

### Step 1: Define the total time
Let the total time taken by the car be \( t \).

### Step 2: Divide the total time into two halves
The car travels for the first half of the time \( \frac{t}{2} \) with a speed of \( 40 \, \text{km/h} \) and for the second half of the time \( \frac{t}{2} \) with a speed of \( 60 \, \text{km/h} \).

### Step 3: Calculate the distance traveled in each half
- For the first half of the time:
\[ s_1 = \text{speed} \times \text{time} = 40 \, \text{km/h} \times \frac{t}{2} = 20t \, \text{km} \]

- For the second half of the time:
\[ s_2 = \text{speed} \times \text{time} = 60 \, \text{km/h} \times \frac{t}{2} = 30t \, \text{km} \]

### Step 4: Calculate the total distance
The total distance \( S \) traveled by the car is the sum of the distances from both halves:
\[ S = s_1 + s_2 = 20t + 30t = 50t \, \text{km} \]

### Step 5: Calculate the average speed
The average speed \( V_{avg} \) is given by the formula:
\[ V_{avg} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{S}{t} \]
Substituting the values we found:
\[ V_{avg} = \frac{50t}{t} = 50 \, \text{km/h} \]

### Conclusion
The average speed of the car is \( 50 \, \text{km/h} \).

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