If P travelled the first half of a journey at 40 km/hr and the remaining half distance at 50 km/hr, what is the average speed of his travel ?
A. `44.44` km/hr
B. `53.33` km/hr
C. 45 km/hr
D. 60 km/hr

Options

A. D
B. A
C. C
D. B

Answer

To find the average speed of P's journey, we can follow these steps:

### Step 1: Define the total distance
Let the total distance of the journey be \( x \) km.

### Step 2: Calculate the distance for each half
Since P travels half of the distance at 40 km/hr and the other half at 50 km/hr, the distance for each half will be:
- First half distance = \( \frac{x}{2} \) km
- Second half distance = \( \frac{x}{2} \) km

### Step 3: Calculate the time taken for each half
Now, we need to calculate the time taken for each half of the journey:
- Time for the first half = \( \text{Distance} \div \text{Speed} = \frac{\frac{x}{2}}{40} = \frac{x}{80} \) hours
- Time for the second half = \( \text{Distance} \div \text{Speed} = \frac{\frac{x}{2}}{50} = \frac{x}{100} \) hours

### Step 4: Calculate the total time taken
Now, we can find the total time taken for the entire journey:
\[ \text{Total time} = \text{Time for first half} + \text{Time for second half} = \frac{x}{80} + \frac{x}{100} \]

### Step 5: Find a common denominator and simplify
To add the fractions, we need a common denominator. The least common multiple of 80 and 100 is 400.
\[ \frac{x}{80} = \frac{5x}{400}, \quad \frac{x}{100} = \frac{4x}{400} \]
So,
\[ \text{Total time} = \frac{5x}{400} + \frac{4x}{400} = \frac{9x}{400} \text{ hours} \]

### Step 6: Calculate the average speed
The average speed is given by the formula:
\[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{x}{\frac{9x}{400}} = \frac{x \cdot 400}{9x} = \frac{400}{9} \text{ km/hr} \]

### Step 7: Calculate the numerical value
Now, we can calculate \( \frac{400}{9} \):
\[ \frac{400}{9} \approx 44.44 \text{ km/hr} \]

### Conclusion
Thus, the average speed of P's travel is approximately \( 44.44 \) km/hr.