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 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 distance and total time
- The total distance covered by the car is given as \( D = 60 \, \text{km} \).

### Step 2: Define the speeds and time intervals
- The car travels for half of its time at a speed of \( v_1 = 80 \, \text{km/h} \) and for the other half at \( v_2 = 40 \, \text{km/h} \).
- Let the total time taken by the car be \( t \). Therefore, the time spent at each speed is \( \frac{t}{2} \).

### Step 3: Calculate the distance covered at each speed
- The distance covered during the first half of the time is:
\[ d_1 = v_1 \times \frac{t}{2} = 80 \times \frac{t}{2} = 40t \, \text{km} \]
- The distance covered during the second half of the time is:
\[ d_2 = v_2 \times \frac{t}{2} = 40 \times \frac{t}{2} = 20t \, \text{km} \]

### Step 4: Set up the equation for total distance
- The total distance covered is the sum of the distances covered at both speeds:
\[ d_1 + d_2 = 60 \, \text{km} \]
Substituting the expressions for \( d_1 \) and \( d_2 \):
\[ 40t + 20t = 60 \]
Simplifying this gives:
\[ 60t = 60 \]

### Step 5: Solve for total time \( t \)
- Dividing both sides by 60:
\[ t = 1 \, \text{hour} \]

### Step 6: Calculate the average speed
- The average speed \( v_{avg} \) is defined as the total distance divided by the total time:
\[ v_{avg} = \frac{D}{t} = \frac{60 \, \text{km}}{1 \, \text{hour}} = 60 \, \text{km/h} \]

### Final Answer
The average speed of the car is \( 60 \, \text{km/h} \).

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