A car covers first 10 km with 40 km/hr next 10 km with 60 km/hr and next 10 km in 20 km/hr . What is the average speed of the car .

Options

A. 320/11
B. 330/11
C. 350/11
D. 360/11

Explanation

To find the average speed of the car over the entire journey, we need to follow these steps:

### Step 1: Calculate the total distance traveled
The car covers three segments of 10 km each:
- First segment: 10 km
- Second segment: 10 km
- Third segment: 10 km

**Total Distance = 10 km + 10 km + 10 km = 30 km**

### Step 2: Calculate the time taken for each segment
We will calculate the time taken for each segment using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

1. **For the first segment (10 km at 40 km/hr)**:
\[ \text{Time}_1 = \frac{10 \text{ km}}{40 \text{ km/hr}} = \frac{1}{4} \text{ hr} = 0.25 \text{ hr} \]

2. **For the second segment (10 km at 60 km/hr)**:
\[ \text{Time}_2 = \frac{10 \text{ km}}{60 \text{ km/hr}} = \frac{1}{6} \text{ hr} \approx 0.1667 \text{ hr} \]

3. **For the third segment (10 km at 20 km/hr)**:
\[ \text{Time}_3 = \frac{10 \text{ km}}{20 \text{ km/hr}} = \frac{1}{2} \text{ hr} = 0.5 \text{ hr} \]

### Step 3: Calculate the total time taken
Now, we add the time taken for each segment:
\[ \text{Total Time} = \text{Time}_1 + \text{Time}_2 + \text{Time}_3 = 0.25 \text{ hr} + \frac{1}{6} \text{ hr} + 0.5 \text{ hr} \]

To add these fractions, we find a common denominator. The LCM of 4, 6, and 2 is 12:
- Convert \(0.25\) to twelfths: \(0.25 = \frac{3}{12}\)
- Convert \(\frac{1}{6}\) to twelfths: \(\frac{1}{6} = \frac{2}{12}\)
- Convert \(0.5\) to twelfths: \(0.5 = \frac{6}{12}\)

Now, adding them:
\[ \text{Total Time} = \frac{3}{12} + \frac{2}{12} + \frac{6}{12} = \frac{11}{12} \text{ hr} \]

### Step 4: Calculate the average speed
The average speed is given by the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]
Substituting the values we found:
\[ \text{Average Speed} = \frac{30 \text{ km}}{\frac{11}{12} \text{ hr}} = 30 \times \frac{12}{11} = \frac{360}{11} \text{ km/hr} \]

### Final Answer
The average speed of the car is \(\frac{360}{11} \text{ km/hr}\) or approximately \(32.73 \text{ km/hr}\).

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