A car moving on a straight road covers 1/3 of the distance with 25 km / h and rest with 75 km/h . The average speed (in km `h^(-1)`) is ________

Explanation

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

### Step 1: Define the total distance
Let the total distance \( S \) be divided into two parts:
- The first part \( AB \) covers \( \frac{1}{3}S \) at a speed of \( 25 \) km/h.
- The second part \( BC \) covers \( \frac{2}{3}S \) at a speed of \( 75 \) km/h.

### Step 2: Calculate the time taken for each part
1. **Time for the first part (T1)**:
\[ T_1 = \frac{\text{Distance}}{\text{Speed}} = \frac{\frac{1}{3}S}{25} \]
Simplifying this gives:
\[ T_1 = \frac{S}{75} \text{ hours} \]

2. **Time for the second part (T2)**:
\[ T_2 = \frac{\text{Distance}}{\text{Speed}} = \frac{\frac{2}{3}S}{75} \]
Simplifying this gives:
\[ T_2 = \frac{2S}{225} \text{ hours} \]

### Step 3: Calculate the total time taken
Now, we can find the total time \( T \):
\[ T = T_1 + T_2 = \frac{S}{75} + \frac{2S}{225} \]
To add these fractions, we need a common denominator. The least common multiple of \( 75 \) and \( 225 \) is \( 225 \):
\[ T = \frac{3S}{225} + \frac{2S}{225} = \frac{5S}{225} = \frac{S}{45} \text{ hours} \]

### Step 4: Calculate the average speed
The average speed \( V_{avg} \) is given by the formula:
\[ V_{avg} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{S}{\frac{S}{45}} = 45 \text{ km/h} \]

### Final Answer
The average speed of the car is \( 45 \) km/h.

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