A man rows 25 km downstream and 20 km upstream taking 5 h each time . What is the velocity of the current ?

Options

A. 1 km/h
B. 2.5 km/h
C. 3.5 km/h
D. None of these

Explanation

To solve the problem step by step, we will use the concepts of speed, distance, and time.

### Step 1: Understand the Problem
We have a man rowing downstream and upstream. The distance he rows downstream is 25 km, and the distance upstream is 20 km. He takes 5 hours for each journey.

### Step 2: Calculate Downstream Speed
Using the formula for speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
For downstream:
- Distance = 25 km
- Time = 5 hours

Calculating the downstream speed:
\[ \text{Downstream Speed} = \frac{25 \text{ km}}{5 \text{ h}} = 5 \text{ km/h} \]

### Step 3: Calculate Upstream Speed
Now, we calculate the speed for upstream:
- Distance = 20 km
- Time = 5 hours

Calculating the upstream speed:
\[ \text{Upstream Speed} = \frac{20 \text{ km}}{5 \text{ h}} = 4 \text{ km/h} \]

### Step 4: Set Up the Equations
Let \( v \) be the speed of the man in still water and \( c \) be the speed of the current. We can set up the following equations based on the downstream and upstream speeds:
- Downstream: \( v + c = 5 \)
- Upstream: \( v - c = 4 \)

### Step 5: Solve the Equations
Now we can solve these two equations simultaneously.

1. From the first equation:
\[ v + c = 5 \quad \text{(1)} \]

2. From the second equation:
\[ v - c = 4 \quad \text{(2)} \]

Adding equations (1) and (2):
\[ (v + c) + (v - c) = 5 + 4 \]
\[ 2v = 9 \implies v = 4.5 \text{ km/h} \]

Now substituting \( v = 4.5 \) into equation (1):
\[ 4.5 + c = 5 \implies c = 5 - 4.5 = 0.5 \text{ km/h} \]

### Step 6: Conclusion
The velocity of the current is:
\[ \text{Velocity of the current} = 0.5 \text{ km/h} \]

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