One car moving on a straight 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 2/3`km/hr
D. 36 km/hr

Answer

To find the average speed of the car that covers one-third of the distance at 20 km/hr and the remaining two-thirds at 60 km/hr, we can follow these steps:

### Step 1: Define the total distance
Let the total distance be \( S \).

### Step 2: Calculate the distance for each segment
- The distance covered at 20 km/hr is \( \frac{S}{3} \).
- The distance covered at 60 km/hr is \( \frac{2S}{3} \).

### Step 3: Calculate the time taken for each segment
- Time taken for the first segment (at 20 km/hr):
\[ t_1 = \frac{\text{Distance}}{\text{Speed}} = \frac{\frac{S}{3}}{20} = \frac{S}{60} \text{ hours} \]

- Time taken for the second segment (at 60 km/hr):
\[ t_2 = \frac{\text{Distance}}{\text{Speed}} = \frac{\frac{2S}{3}}{60} = \frac{2S}{180} = \frac{S}{90} \text{ hours} \]

### Step 4: Calculate the total time taken
The total time \( T \) taken for the entire journey is:
\[ T = t_1 + t_2 = \frac{S}{60} + \frac{S}{90} \]

### Step 5: Find a common denominator to add the times
The least common multiple of 60 and 90 is 180. We can rewrite the times:
\[ T = \frac{3S}{180} + \frac{2S}{180} = \frac{5S}{180} = \frac{S}{36} \text{ hours} \]

### Step 6: Calculate the average speed
Average speed is defined as the total distance divided by the total time. Therefore:
\[ \text{Average Speed} = \frac{S}{T} = \frac{S}{\frac{S}{36}} = 36 \text{ km/hr} \]

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

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