A car completes a journery in 10 hours. If it covers half of the journey at 40 kmph and the remaining half at 60 kmph, the distance covered by car is

Options

A. 400km
B. 480km
C. 380km
D. 300km

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Define the total distance
Let the total distance of the journey be \( 2x \) kilometers. This means half of the journey is \( x \) kilometers.

**Hint:** Define the total distance in terms of a variable to simplify calculations.

### Step 2: Calculate time for each half of the journey
The car covers the first half of the journey (\( x \) kilometers) at a speed of 40 km/h. The time taken for this part is given by the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{x}{40} \]

For the second half of the journey (\( x \) kilometers) at a speed of 60 km/h, the time taken is:
\[ \text{Time} = \frac{x}{60} \]

**Hint:** Use the formula for time to find the time taken for each segment of the journey.

### Step 3: Set up the equation for total time
The total time for the journey is given as 10 hours. Therefore, we can set up the equation:
\[ \frac{x}{40} + \frac{x}{60} = 10 \]

**Hint:** Combine the times for both segments to form a single equation.

### Step 4: Find a common denominator and simplify
The least common multiple (LCM) of 40 and 60 is 120. We can rewrite the equation using this common denominator:
\[ \frac{3x}{120} + \frac{2x}{120} = 10 \]
Combining the fractions gives:
\[ \frac{5x}{120} = 10 \]

**Hint:** Use the LCM to combine fractions easily.

### Step 5: Solve for \( x \)
To eliminate the fraction, multiply both sides by 120:
\[ 5x = 1200 \]
Now, divide both sides by 5:
\[ x = 240 \]

**Hint:** Isolate the variable \( x \) to find its value.

### Step 6: Calculate the total distance
Since \( x \) represents half of the journey, the total distance \( 2x \) is:
\[ 2x = 2 \times 240 = 480 \text{ kilometers} \]

**Hint:** Remember to multiply by 2 to find the total distance.

### Conclusion
The total distance covered by the car is **480 kilometers**.