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. 45 kmph
B. 50 kmph
C. 52.5 kmph
D. 55 kmph

Explanation

To find the average speed of the car, we need to use the formula for average speed, which is the total distance traveled divided by the total time taken. Let's break down the problem step by step.

### Step-by-Step Solution:

1. **Define Variables:**
- Let the total time of travel be \( t \).
- The car travels for the first half of the time, \( t/2 \), with a speed of \( 40 \, \text{km/h} \).
- The car travels for the second half of the time, \( t/2 \), with a speed of \( 60 \, \text{km/h} \).

2. **Calculate the Distance Traveled in the First Half:**
- Speed \( v_1 = 40 \, \text{km/h} \)
- Time \( t_1 = t/2 \)
- Distance \( s_1 = v_1 \times t_1 \)
\[ s_1 = 40 \, \text{km/h} \times \frac{t}{2} = 20t \, \text{km} \]

3. **Calculate the Distance Traveled in the Second Half:**
- Speed \( v_2 = 60 \, \text{km/h} \)
- Time \( t_2 = t/2 \)
- Distance \( s_2 = v_2 \times t_2 \)
\[ s_2 = 60 \, \text{km/h} \times \frac{t}{2} = 30t \, \text{km} \]

4. **Calculate the Total Distance Traveled:**
\[ \text{Total Distance} = s_1 + s_2 = 20t + 30t = 50t \, \text{km} \]

5. **Calculate the Total Time Taken:**
\[ \text{Total Time} = t \]

6. **Calculate the Average Speed:**
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{50t \, \text{km}}{t \, \text{hours}} = 50 \, \text{km/h} \]

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