A motor car covers `1//3^(rd)` part of total distance with
` v_(1) = 10 km//hr` , second `1//3^(rd )` part with `v_(2) = 20 ` km/hr and rest ` 1//3^(rd)` part with `v_(3)=60` km/hr. What is the average speed of the car?

Options

A. 18 km/hr
B. 45 km/hr
C. 6km/hr
D. 22. 5 km/hr

Answer

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

### Step 1: Define the total distance
Let the total distance covered by the car be \( d \) km. Since the car covers this distance in three equal parts, each part will be \( \frac{d}{3} \) km.

### Step 2: Calculate the time taken for each part of the journey
1. **For the first part** (distance = \( \frac{d}{3} \), speed = \( v_1 = 10 \) km/hr):
\[ t_1 = \frac{\text{Distance}}{\text{Speed}} = \frac{\frac{d}{3}}{10} = \frac{d}{30} \text{ hours} \]

2. **For the second part** (distance = \( \frac{d}{3} \), speed = \( v_2 = 20 \) km/hr):
\[ t_2 = \frac{\frac{d}{3}}{20} = \frac{d}{60} \text{ hours} \]

3. **For the third part** (distance = \( \frac{d}{3} \), speed = \( v_3 = 60 \) km/hr):
\[ t_3 = \frac{\frac{d}{3}}{60} = \frac{d}{180} \text{ hours} \]

### Step 3: Calculate the total time taken
Now, we can find the total time \( T \) taken for the entire journey:
\[ T = t_1 + t_2 + t_3 = \frac{d}{30} + \frac{d}{60} + \frac{d}{180} \]

To add these fractions, we need a common denominator. The least common multiple (LCM) of 30, 60, and 180 is 180. Now we convert each term:
\[ T = \frac{6d}{180} + \frac{3d}{180} + \frac{d}{180} = \frac{10d}{180} = \frac{d}{18} \text{ hours} \]

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

Thus, the average speed of the car is **18 km/hr**.