A car is moving on a straight road covers one third of the distance with a speed of 20 km/h and the rest with a speed of 60 km/h. The average speed of the car is

Options

A. 40 km/h
B. 50 km/h
C. 36 km/h
D. 55 km/h

Answer

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

### Step 1: Define the total distance
Let the total distance covered by the car be \( x \) kilometers.

### Step 2: Calculate the distance covered at each speed
The car covers one third of the distance at a speed of 20 km/h. Therefore, the distance covered at this speed is:
\[ \text{Distance}_1 = \frac{x}{3} \]
The remaining distance, which is two thirds of the total distance, is covered at a speed of 60 km/h:
\[ \text{Distance}_2 = \frac{2x}{3} \]

### Step 3: Calculate the time taken for each segment
The time taken to cover the first distance is given by:
\[ \text{Time}_1 = \frac{\text{Distance}_1}{\text{Speed}_1} = \frac{\frac{x}{3}}{20} = \frac{x}{60} \text{ hours} \]
The time taken to cover the second distance is given by:
\[ \text{Time}_2 = \frac{\text{Distance}_2}{\text{Speed}_2} = \frac{\frac{2x}{3}}{60} = \frac{2x}{180} = \frac{x}{90} \text{ hours} \]

### Step 4: Calculate the total time taken
The total time taken for the journey is:
\[ \text{Total Time} = \text{Time}_1 + \text{Time}_2 = \frac{x}{60} + \frac{x}{90} \]
To add these fractions, we need a common denominator. The least common multiple of 60 and 90 is 180. Thus, we can rewrite the times:
\[ \text{Total Time} = \frac{3x}{180} + \frac{2x}{180} = \frac{5x}{180} = \frac{x}{36} \text{ hours} \]

### Step 5: Calculate the average speed
The average speed is defined as the total distance divided by the total time:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{x}{\frac{x}{36}} = 36 \text{ km/h} \]

Thus, the average speed of the car is **36 km/h**.

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