A man can row 6 km/h in still water. If the speed of the current is 2 km/h, it takes 3 hours more in upstream than in the downstream for the same distance. The distance is

Options

A. 30 km
B. 24km
C. 20 km
D. 32km

Answer

To solve the problem step by step, we will analyze the situation involving the rowing speed of the man, the speed of the current, and the time taken for upstream and downstream travel.

### Step 1: Understand the given information
- The man's rowing speed in still water = 6 km/h
- The speed of the current = 2 km/h
- The time difference between upstream and downstream = 3 hours

### Step 2: Calculate downstream and upstream speeds
- **Downstream speed** = Speed in still water + Speed of current
\[ \text{Downstream speed} = 6 \text{ km/h} + 2 \text{ km/h} = 8 \text{ km/h} \]

- **Upstream speed** = Speed in still water - Speed of current
\[ \text{Upstream speed} = 6 \text{ km/h} - 2 \text{ km/h} = 4 \text{ km/h} \]

### Step 3: Set up the time equations
Let the distance be \( x \) km. The time taken to travel downstream and upstream can be expressed as:
- **Time taken downstream** = \( \frac{x}{8} \) hours
- **Time taken upstream** = \( \frac{x}{4} \) hours

### Step 4: Set up the equation based on the time difference
According to the problem, the time taken upstream is 3 hours more than the time taken downstream:
\[ \frac{x}{4} - \frac{x}{8} = 3 \]

### Step 5: Solve the equation
To solve the equation, first find a common denominator (which is 8):
\[ \frac{2x}{8} - \frac{x}{8} = 3 \]
This simplifies to:
\[ \frac{2x - x}{8} = 3 \]
\[ \frac{x}{8} = 3 \]
Now, multiply both sides by 8:
\[ x = 3 \times 8 \]
\[ x = 24 \]

### Step 6: Conclusion
The distance \( x \) is 24 km.

### Final Answer
The distance is **24 km**.

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