A car moves for half of its time at `80 km//h` and for rest of time at `40 km//h`. Total distance covered is `60km`. What is the average speed of the car

Options

A. `60 kmh^(-1)`
B. `80 kmh^(-1)`
C. `120 kmh^(-1)`
D. `180 kmh^(-1)`

Explanation

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

### Step 1: Understand the problem
The car travels for half of the total time at a speed of 80 km/h and for the other half at a speed of 40 km/h. The total distance covered by the car is 60 km.

### Step 2: Define the total time
Let the total time of travel be \( t \). Therefore, the car travels for \( \frac{t}{2} \) at 80 km/h and \( \frac{t}{2} \) at 40 km/h.

### Step 3: Calculate the distances covered in each segment
1. **Distance covered at 80 km/h**:
\[ \text{Distance}_1 = \text{Speed} \times \text{Time} = 80 \, \text{km/h} \times \frac{t}{2} = 40t \, \text{km} \]

2. **Distance covered at 40 km/h**:
\[ \text{Distance}_2 = \text{Speed} \times \text{Time} = 40 \, \text{km/h} \times \frac{t}{2} = 20t \, \text{km} \]

### Step 4: Set up the equation for total distance
The total distance covered by the car is the sum of the two distances:
\[ \text{Total Distance} = \text{Distance}_1 + \text{Distance}_2 = 40t + 20t = 60t \, \text{km} \]
According to the problem, this total distance is equal to 60 km:
\[ 60t = 60 \]

### Step 5: Solve for \( t \)
\[ t = 1 \, \text{hour} \]

### Step 6: Calculate the total time taken
Since \( t = 1 \, \text{hour} \), the total time taken is 1 hour.

### Step 7: Calculate the average speed
The average speed is given by the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{60 \, \text{km}}{1 \, \text{hour}} = 60 \, \text{km/h} \]

### Final Answer:
The average speed of the car is **60 km/h**.

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