One car moving on a staright road covers one-third of the distance with 20 `(km)/(hr)` and the rest with 60 `(km)/(hr)`. The average speed is

Options

A. 40 `(km)/(hr)`
B. 80 `(km)/(hr)`
C. `46(1)/(2)(km)/(hr)`
D. 36 `(km)/(hr)`

Explanation

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

### Step 1: Define the total distance
Let's assume the total distance covered by the car is \( D \) kilometers. According to the problem, the car covers one-third of this distance at a speed of 20 km/hr and the remaining two-thirds at a speed of 60 km/hr.

### Step 2: Calculate the distance for each segment
- Distance for the first segment (one-third of total distance):
\[ D_1 = \frac{D}{3} \]
- Distance for the second segment (two-thirds of total distance):
\[ D_2 = \frac{2D}{3} \]

### Step 3: Calculate the time taken for each segment
- Time taken to cover the first segment at 20 km/hr:
\[ T_1 = \frac{D_1}{\text{Speed}} = \frac{\frac{D}{3}}{20} = \frac{D}{60} \text{ hours} \]
- Time taken to cover the second segment at 60 km/hr:
\[ T_2 = \frac{D_2}{\text{Speed}} = \frac{\frac{2D}{3}}{60} = \frac{2D}{180} = \frac{D}{90} \text{ hours} \]

### Step 4: Calculate the total time taken
Now, we can find the total time taken for the entire journey:
\[ T_{\text{total}} = T_1 + T_2 = \frac{D}{60} + \frac{D}{90} \]

To add these fractions, we need a common denominator:
- The least common multiple of 60 and 90 is 180.
- Convert both fractions:
\[ T_1 = \frac{D}{60} = \frac{3D}{180} \]
\[ T_2 = \frac{D}{90} = \frac{2D}{180} \]

Now adding:
\[ T_{\text{total}} = \frac{3D}{180} + \frac{2D}{180} = \frac{5D}{180} = \frac{D}{36} \text{ hours} \]

### Step 5: Calculate the average speed
The average speed is given by the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{D}{T_{\text{total}}} \]
Substituting the values we have:
\[ \text{Average Speed} = \frac{D}{\frac{D}{36}} = 36 \text{ km/hr} \]

### Conclusion
The average speed of the car is **36 km/hr**.

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