An automobile driver travels from a plain to a hill station 120 km away at an average speed of 30 km per hour. He then makes the return trip at an average speed 25 km per hour. He covers another 120 km on the plain at an average speed of 50 km per hour. His average speed (in km/hr) over the entire distance of 360 km will be

Options

A. `(30+25+50)/(3)`
B. `((a)/(30)+(1)/(25)+(1)/(50))/(3)`
C. `(3)/((1)/(30)+(1)/(25)+(1)/(50))`
D. None of these

Explanation

To find the average speed of the automobile driver over the entire distance of 360 km, we will follow these steps:

### Step 1: Calculate the time taken for each segment of the journey.

1. **From the plain to the hill station (120 km at 30 km/hr)**:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{120 \text{ km}}{30 \text{ km/hr}} = 4 \text{ hours} \]

2. **Return trip from the hill station to the plain (120 km at 25 km/hr)**:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{120 \text{ km}}{25 \text{ km/hr}} = 4.8 \text{ hours} \]

3. **On the plain (120 km at 50 km/hr)**:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{120 \text{ km}}{50 \text{ km/hr}} = 2.4 \text{ hours} \]

### Step 2: Calculate the total time taken for the entire journey.

\[ \text{Total Time} = 4 \text{ hours} + 4.8 \text{ hours} + 2.4 \text{ hours} = 11.2 \text{ hours} \]

### Step 3: Calculate the average speed over the entire distance.

The average speed is calculated using the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]

Substituting the values:
\[ \text{Average Speed} = \frac{360 \text{ km}}{11.2 \text{ hours}} \approx 32.14 \text{ km/hr} \]

### Final Answer:
The average speed over the entire distance of 360 km is approximately **32.14 km/hr**.

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