Out of the total distance of 180 km, a car travels one third of it at a speed of 30 km/hr and remaining distance at the speed of 40 kmph. What is the average speed of the car ? (in km/hr)

Options

A. 38
B. 35
C. 36
D. 32

Answer

To find the average speed of the car over a total distance of 180 km, where it travels one-third of the distance at a speed of 30 km/hr and the remaining distance at a speed of 40 km/hr, we can follow these steps:

### Step 1: Calculate the distance traveled at each speed
The total distance is 180 km. The car travels one-third of this distance at 30 km/hr.

\[ \text{Distance traveled at 30 km/hr} = \frac{1}{3} \times 180 = 60 \text{ km} \]

The remaining distance is:

\[ \text{Remaining distance} = 180 - 60 = 120 \text{ km} \]

### Step 2: Calculate the time taken to travel each distance
**Time taken to travel 60 km at 30 km/hr:**

Using the formula for time, which is:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

We find:

\[ \text{Time}_{30} = \frac{60 \text{ km}}{30 \text{ km/hr}} = 2 \text{ hours} \]

**Time taken to travel 120 km at 40 km/hr:**

\[ \text{Time}_{40} = \frac{120 \text{ km}}{40 \text{ km/hr}} = 3 \text{ hours} \]

### Step 3: Calculate the total time taken
Now, we add the time taken for both segments of the journey:

\[ \text{Total time} = \text{Time}_{30} + \text{Time}_{40} = 2 \text{ hours} + 3 \text{ hours} = 5 \text{ hours} \]

### 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 have:

\[ \text{Average Speed} = \frac{180 \text{ km}}{5 \text{ hours}} = 36 \text{ km/hr} \]

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

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