A car covers a certain distance in 8 hrs. It covers half distance at the speed of 40 km/hr and the other half at the speed of 60 km/hr. Find the distance of the journey.

Options

A. 384 kms
B. 368 kms
C. 388 kms
D. 344 kms

Answer

To solve the problem, we need to find the total distance of the journey based on the information given about the speeds and the time taken.

### Step 1: Define the total distance
Let the total distance of the journey be \( D \). According to the problem, the car covers half of this distance at a speed of 40 km/hr and the other half at a speed of 60 km/hr.

### Step 2: Calculate half of the distance
Since \( D \) is the total distance, half of the distance is:
\[ \text{Half distance} = \frac{D}{2} \]

### Step 3: Calculate time taken for each half of the journey
1. **Time taken to cover the first half at 40 km/hr:**
\[ \text{Time}_1 = \frac{\text{Distance}}{\text{Speed}} = \frac{\frac{D}{2}}{40} = \frac{D}{80} \text{ hours} \]

2. **Time taken to cover the second half at 60 km/hr:**
\[ \text{Time}_2 = \frac{\text{Distance}}{\text{Speed}} = \frac{\frac{D}{2}}{60} = \frac{D}{120} \text{ hours} \]

### Step 4: Set up the equation for total time
The total time taken for the journey is given as 8 hours. Therefore, we can write:
\[ \text{Total Time} = \text{Time}_1 + \text{Time}_2 \]
Substituting the values we calculated:
\[ \frac{D}{80} + \frac{D}{120} = 8 \]

### Step 5: Find a common denominator and solve for \( D \)
The common denominator for 80 and 120 is 240. We can rewrite the equation:
\[ \frac{3D}{240} + \frac{2D}{240} = 8 \]
Combining the fractions:
\[ \frac{5D}{240} = 8 \]
Now, multiply both sides by 240:
\[ 5D = 8 \times 240 \]
Calculating the right side:
\[ 5D = 1920 \]
Now, divide both sides by 5:
\[ D = \frac{1920}{5} = 384 \]

### Step 6: Conclusion
The total distance of the journey is:
\[ \boxed{384 \text{ km}} \]

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