John travels `{:(2)/(3):}"rd"` of a distance by bike and remaining 6 km on foot . How many km does he travels in the whole journey ?

Options

A. 28 km
B. 18 km
C. 26 km
D. 14 km

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define the total distance
Let the total distance John travels be represented by \( x \) kilometers.

### Step 2: Determine the distance traveled by bike
According to the problem, John travels \( \frac{2}{3} \) of the total distance by bike. Therefore, the distance he travels by bike is:
\[ \text{Distance by bike} = \frac{2}{3}x \]

### Step 3: Determine the remaining distance
The remaining distance, which John travels on foot, is given as 6 km. Since he travels \( \frac{2}{3} \) of the distance by bike, the remaining distance can be calculated as:
\[ \text{Remaining distance} = x - \frac{2}{3}x \]

### Step 4: Simplify the remaining distance
Now, simplify the expression for the remaining distance:
\[ \text{Remaining distance} = x - \frac{2}{3}x = \frac{3}{3}x - \frac{2}{3}x = \frac{1}{3}x \]

### Step 5: Set up the equation
Since we know that the remaining distance is 6 km, we can set up the equation:
\[ \frac{1}{3}x = 6 \]

### Step 6: Solve for \( x \)
To find \( x \), multiply both sides of the equation by 3:
\[ x = 6 \times 3 = 18 \]

### Step 7: Conclusion
Thus, the total distance John travels in the whole journey is:
\[ \text{Total distance} = 18 \text{ km} \]