A man can row a certain distance against the stream in six hours. However, he would take two hours less to cover the same distance with the current. If the speed of the current is 2 kmph, then what is the rowing speed in still water?

Options

A. 10 kmph
B. 12 kmph
C. 14 kmph
D. 8 kmph

Answer

To solve the problem, we will break it down step by step.

### Step 1: Define Variables
Let:
- \( x \) = rowing speed in still water (in km/h)
- Speed of the current = 2 km/h

### Step 2: Determine Upstream and Downstream Speeds
- Upstream speed (against the current) = \( x - 2 \) km/h
- Downstream speed (with the current) = \( x + 2 \) km/h

### Step 3: Set Up Time Equations
From the problem:
- Time taken to row upstream = 6 hours
- Time taken to row downstream = 4 hours (since it takes 2 hours less)

Let the distance be \( d \) km. We can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

For upstream:
\[ 6 = \frac{d}{x - 2} \quad \text{(1)} \]

For downstream:
\[ 4 = \frac{d}{x + 2} \quad \text{(2)} \]

### Step 4: Express Distance in Terms of Speed
From equation (1):
\[ d = 6(x - 2) \quad \text{(3)} \]

From equation (2):
\[ d = 4(x + 2) \quad \text{(4)} \]

### Step 5: Set Equations for Distance Equal
Since both equations (3) and (4) represent the same distance \( d \):
\[ 6(x - 2) = 4(x + 2) \]

### Step 6: Solve for \( x \)
Expanding both sides:
\[ 6x - 12 = 4x + 8 \]

Rearranging gives:
\[ 6x - 4x = 8 + 12 \]
\[ 2x = 20 \]
\[ x = 10 \text{ km/h} \]

### Step 7: Conclusion
The rowing speed in still water is \( 10 \) km/h.

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