From a starting point A, Rahul walks 3/4 km towards east and then 6/7 km towards west to reach point C.
How much more distance he travelled towards west than east ?

Options

A. `(-9)/(28)`
B. `(3)/(28)`
C. `(9)/(28)`
D. `(-3)/(28)`

Answer

To solve the problem step by step, we need to find out how much more distance Rahul traveled towards the west compared to the east.

### Step 1: Identify the distances traveled
Rahul walks:
- \( \frac{3}{4} \) km towards the east
- \( \frac{6}{7} \) km towards the west

### Step 2: Set up the equation to find the difference
To find out how much more distance he traveled towards the west than east, we need to subtract the distance traveled east from the distance traveled west.

The equation will be:
\[ \text{Extra distance towards west} = \text{Distance towards west} - \text{Distance towards east} \]
Substituting the values:
\[ \text{Extra distance towards west} = \frac{6}{7} - \frac{3}{4} \]

### Step 3: Find a common denominator
To subtract these fractions, we need a common denominator. The denominators are 7 and 4. The least common multiple (LCM) of 7 and 4 is 28.

### Step 4: Convert the fractions
Now we convert both fractions to have a denominator of 28:
- For \( \frac{6}{7} \):
\[ \frac{6}{7} = \frac{6 \times 4}{7 \times 4} = \frac{24}{28} \]
- For \( \frac{3}{4} \):
\[ \frac{3}{4} = \frac{3 \times 7}{4 \times 7} = \frac{21}{28} \]

### Step 5: Perform the subtraction
Now we can subtract the two fractions:
\[ \text{Extra distance towards west} = \frac{24}{28} - \frac{21}{28} = \frac{24 - 21}{28} = \frac{3}{28} \]

### Step 6: Conclusion
Rahul traveled \( \frac{3}{28} \) km more towards the west than towards the east.

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