A covered half of his journey at 20 km/h and rest at the x km/h then his average speed is 24 km/h.What is the value of x?

Options

A. 30
B. 32
C. 36
D. 40

Answer

To solve the problem, we need to find the value of \( x \) given that a person covers half of his journey at 20 km/h and the other half at \( x \) km/h, resulting in an average speed of 24 km/h.

### Step 1: Understand the average speed formula
The average speed for a journey can be calculated using the formula:
\[ \text{Average Speed} = \frac{2ab}{a + b} \]
where \( a \) and \( b \) are the speeds for the two halves of the journey.

### Step 2: Assign values to \( a \) and \( b \)
In this case, let:
- \( a = 20 \) km/h (speed for the first half)
- \( b = x \) km/h (speed for the second half)

### Step 3: Substitute the values into the average speed formula
We know the average speed is 24 km/h, so we can set up the equation:
\[ 24 = \frac{2 \cdot 20 \cdot x}{20 + x} \]

### Step 4: Simplify the equation
Now, we can simplify the equation:
\[ 24(20 + x) = 40x \]
Expanding the left side:
\[ 480 + 24x = 40x \]

### Step 5: Rearrange the equation
Now, we can rearrange the equation to isolate \( x \):
\[ 480 = 40x - 24x \]
\[ 480 = 16x \]

### Step 6: Solve for \( x \)
Now, divide both sides by 16:
\[ x = \frac{480}{16} = 30 \]

### Conclusion
The value of \( x \) is 30 km/h.