A man can row at 5 kmph . In still water . If the velocity of current is 1 kmph . And it takes him 1 hour to row to a place and come back , how far is the place ?

Options

A. 2.5 km
B. 3 km
C. 2.4 km
D. 3.6 km

Answer

To solve the problem step by step, we will calculate the distance to the place based on the given information about the man's rowing speed and the current's velocity.

### Step 1: Identify the speeds
- The speed of the man in still water (boat speed) = 5 km/h
- The speed of the current = 1 km/h

### Step 2: Calculate the downstream speed
The downstream speed (when rowing with the current) is calculated as:
\[ \text{Downstream Speed (DSS)} = \text{Boat Speed} + \text{Current Speed} \]
\[ \text{DSS} = 5 \text{ km/h} + 1 \text{ km/h} = 6 \text{ km/h} \]

### Step 3: Calculate the upstream speed
The upstream speed (when rowing against the current) is calculated as:
\[ \text{Upstream Speed (USS)} = \text{Boat Speed} - \text{Current Speed} \]
\[ \text{USS} = 5 \text{ km/h} - 1 \text{ km/h} = 4 \text{ km/h} \]

### Step 4: Use the formula for distance
The total time taken to row to the place and come back is given as 1 hour. We can use the formula for distance:
\[ \text{Distance} = \frac{\text{DSS} \times \text{USS}}{\text{DSS} + \text{USS}} \times \text{Time} \]

### Step 5: Substitute the values into the formula
Substituting the values we calculated:
\[ \text{Distance} = \frac{6 \text{ km/h} \times 4 \text{ km/h}}{6 \text{ km/h} + 4 \text{ km/h}} \times 1 \text{ hour} \]

### Step 6: Calculate the distance
Calculating the numerator:
\[ 6 \times 4 = 24 \]
Calculating the denominator:
\[ 6 + 4 = 10 \]
Now substituting these values back into the equation:
\[ \text{Distance} = \frac{24}{10} = 2.4 \text{ km} \]

### Conclusion
The distance to the place is **2.4 km**.

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