A motorist travel to a place 150 m away at an avearge speed of 50 km/hr and returns ar 30 km/hr his average speed for the whole jouney in km/hr is

Options

A. `36.5` km/hr
B. `37.5` km/hr
C. `35.5` km/hr
D. `34.5` km/hr

Answer

To find the average speed of the motorist for the whole journey, we can use the formula for average speed when the distances are the same but the speeds are different for the two parts of the journey.

### Step-by-Step Solution:

1. **Identify the Speeds and Distance**:
- Speed to the destination (A) = 50 km/hr
- Speed on the return (B) = 30 km/hr
- Distance (D) = 150 meters = 0.15 kilometers (since 1 km = 1000 m)

2. **Use the Average Speed Formula**:
The formula for average speed when the distance is the same for both parts of the journey is:
\[ \text{Average Speed} = \frac{2AB}{A + B} \]
where A is the speed to the destination and B is the speed on the return.

3. **Substitute the Values into the Formula**:
\[ \text{Average Speed} = \frac{2 \times 50 \times 30}{50 + 30} \]

4. **Calculate the Numerator**:
\[ 2 \times 50 \times 30 = 3000 \]

5. **Calculate the Denominator**:
\[ 50 + 30 = 80 \]

6. **Calculate the Average Speed**:
\[ \text{Average Speed} = \frac{3000}{80} = 37.5 \text{ km/hr} \]

### Final Answer:
The average speed for the whole journey is **37.5 km/hr**.