A car travels half of the distance with constant velocity 100 km/h and another half with a constant velocity of 60 km/h along a straight line. The average velocity of the car is

Answer

To find the average velocity of the car that travels half of the distance at a speed of 100 km/h and the other half at a speed of 60 km/h, we can follow these steps:

### Step 1: Define the total distance
Let the total distance traveled by the car be \( D \). Since the car travels half of the distance at each speed, we can denote the distance for each segment as:
- Distance for the first half: \( d = \frac{D}{2} \)
- Distance for the second half: \( d = \frac{D}{2} \)

### Step 2: Calculate the time taken for each segment
- For the first half of the distance at 100 km/h:
\[ t_1 = \frac{d}{100} = \frac{\frac{D}{2}}{100} = \frac{D}{200} \]

- For the second half of the distance at 60 km/h:
\[ t_2 = \frac{d}{60} = \frac{\frac{D}{2}}{60} = \frac{D}{120} \]

### Step 3: Find the total time taken
The total time \( T \) taken to travel the entire distance is:
\[ T = t_1 + t_2 = \frac{D}{200} + \frac{D}{120} \]

### Step 4: Calculate the total time using LCM
To add the two fractions, we need to find the least common multiple (LCM) of the denominators 200 and 120. The LCM of 200 and 120 is 600. Therefore, we can rewrite the times as:
\[ t_1 = \frac{D}{200} = \frac{3D}{600} \]
\[ t_2 = \frac{D}{120} = \frac{5D}{600} \]

Now, adding these:
\[ T = \frac{3D}{600} + \frac{5D}{600} = \frac{8D}{600} = \frac{D}{75} \]

### Step 5: Calculate the average velocity
The average velocity \( V \) is given by the total distance divided by the total time:
\[ V = \frac{D}{T} = \frac{D}{\frac{D}{75}} = 75 \text{ km/h} \]

### Conclusion
Thus, the average velocity of the car is \( 75 \) km/h.

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