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

Options

A. 60 km/h
B. 80 km/h
C. 120 km/h
D. 180 km/h

Answer

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

### Step 1: Define the total time taken
Let the total time taken by the car to cover the distance of 60 km be \( t_0 \).

### Step 2: Calculate the time for each speed
Since the car travels for half of the time at 80 km/h and half at 40 km/h, the time spent at each speed is:
- Time at 80 km/h: \( \frac{t_0}{2} \)
- Time at 40 km/h: \( \frac{t_0}{2} \)

### Step 3: Calculate the distance covered at each speed
Using the formula \( \text{Distance} = \text{Speed} \times \text{Time} \):
- Distance covered at 80 km/h:
\[ S_1 = 80 \times \frac{t_0}{2} = 40 t_0 \]
- Distance covered at 40 km/h:
\[ S_2 = 40 \times \frac{t_0}{2} = 20 t_0 \]

### Step 4: Set up the equation for total distance
The total distance covered by the car is the sum of the distances covered at both speeds:
\[ S_1 + S_2 = 60 \text{ km} \]
Substituting the values of \( S_1 \) and \( S_2 \):
\[ 40 t_0 + 20 t_0 = 60 \]
\[ 60 t_0 = 60 \]

### Step 5: Solve for \( t_0 \)
Dividing both sides by 60:
\[ t_0 = 1 \text{ hour} \]

### Step 6: Calculate the average speed
The average speed is given by the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{60 \text{ km}}{t_0} \]
Substituting \( t_0 \):
\[ \text{Average Speed} = \frac{60 \text{ km}}{1 \text{ hour}} = 60 \text{ km/h} \]

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

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