A car travels 1/3 of the distance on a straight road with a velocity of 10 km/h, next one-third with a velocity of 20 km/h and the last one-third with a velocity of 60 km/h. Then the average velocity of the car (in km/h) during the whole journey is

Options

A. 30
B. 20
C. 18
D. 15

Explanation

To find the average velocity of the car during the whole journey, we can follow these steps:

### Step 1: Define the total distance
Let's assume the total distance traveled by the car is \( D \). Since the car travels one-third of the distance at each speed, we can express the distance for each segment as:
- First segment: \( \frac{D}{3} \)
- Second segment: \( \frac{D}{3} \)
- Third segment: \( \frac{D}{3} \)

### Step 2: Calculate the time taken for each segment
Using the formula \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \), we can calculate the time taken for each segment:
- For the first segment (speed = 10 km/h):
\[ t_1 = \frac{\frac{D}{3}}{10} = \frac{D}{30} \]

- For the second segment (speed = 20 km/h):
\[ t_2 = \frac{\frac{D}{3}}{20} = \frac{D}{60} \]

- For the third segment (speed = 60 km/h):
\[ t_3 = \frac{\frac{D}{3}}{60} = \frac{D}{180} \]

### Step 3: Calculate the total time taken
Now, we can find the total time taken for the entire journey by adding the times for each segment:
\[ t_{\text{total}} = t_1 + t_2 + t_3 = \frac{D}{30} + \frac{D}{60} + \frac{D}{180} \]

To add these fractions, we need a common denominator. The least common multiple of 30, 60, and 180 is 180. Thus, we can rewrite the fractions:
\[ t_{\text{total}} = \frac{6D}{180} + \frac{3D}{180} + \frac{D}{180} = \frac{(6 + 3 + 1)D}{180} = \frac{10D}{180} = \frac{D}{18} \]

### Step 4: Calculate the average velocity
The average velocity \( V_{\text{avg}} \) is given by the formula:
\[ V_{\text{avg}} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{D}{\frac{D}{18}} = 18 \text{ km/h} \]

### Final Answer
The average velocity of the car during the whole journey is **18 km/h**.

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