A car is moving on a straight road covers one third of the distance with a speed of 30 km/h and the rest with a speed of 50 km/h. The average speed of the car is

Answer

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

### Step 1: Define the total distance
Let the total distance traveled by the car be \( D \). For simplicity, we can assume \( D = 3D \) (where \( D \) is the total distance).

### Step 2: Calculate the distance for each segment
The car covers one-third of the distance at a speed of 30 km/h. Thus, the distance for this segment \( D_1 \) is:
\[ D_1 = \frac{1}{3}D \]
The remaining distance \( D_2 \) is:
\[ D_2 = D - D_1 = D - \frac{1}{3}D = \frac{2}{3}D \]

### Step 3: Calculate the time taken for each segment
The time taken to cover the first segment \( T_1 \) is given by:
\[ T_1 = \frac{D_1}{S_1} = \frac{\frac{1}{3}D}{30} = \frac{D}{90} \text{ hours} \]
The time taken to cover the second segment \( T_2 \) is given by:
\[ T_2 = \frac{D_2}{S_2} = \frac{\frac{2}{3}D}{50} = \frac{2D}{150} = \frac{D}{75} \text{ hours} \]

### Step 4: Calculate the total time taken
The total time \( T \) taken for the journey is:
\[ T = T_1 + T_2 = \frac{D}{90} + \frac{D}{75} \]
To add these fractions, we need a common denominator. The least common multiple of 90 and 75 is 450. Thus:
\[ T = \frac{D \cdot 5}{450} + \frac{D \cdot 6}{450} = \frac{11D}{450} \text{ hours} \]

### Step 5: Calculate the average speed
The average speed \( V \) is given by the total distance divided by the total time:
\[ V = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{D}{T} = \frac{3D}{\frac{11D}{450}} = \frac{3D \cdot 450}{11D} \]
The \( D \) cancels out, giving:
\[ V = \frac{1350}{11} \approx 122.73 \text{ km/h} \]

### Final Answer
Thus, the average speed of the car is approximately \( 122.73 \text{ km/h} \).