A man rows upstream 18 km and downstream 28 km taking 5 h each time. Then, the velocity of the current is

Options

A. 1.5 km/h
B. 4.1 km/h
C. 5,6 km/h
D. None of these

Answer

To solve the problem, we will use the concepts of speed, distance, and time. Let's break it down step by step.

### Step 1: Define Variables
Let:
- \( S \) = speed of the man in still water (in km/h)
- \( V \) = speed of the current (in km/h)

### Step 2: Set Up Equations for Upstream and Downstream
When the man rows upstream (against the current), his effective speed is \( S - V \). When he rows downstream (with the current), his effective speed is \( S + V \).

Given:
- Distance upstream = 18 km
- Distance downstream = 28 km
- Time taken for both upstream and downstream = 5 hours

From the formula \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \), we can set up the following equations:

1. For upstream:
\[ S - V = \frac{18}{5} \quad \text{(1)} \]

2. For downstream:
\[ S + V = \frac{28}{5} \quad \text{(2)} \]

### Step 3: Solve the Equations
Now we have two equations:
1. \( S - V = 3.6 \) (from equation 1)
2. \( S + V = 5.6 \) (from equation 2)

We can solve these equations simultaneously.

### Step 4: Add the Two Equations
Adding equations (1) and (2):
\[ (S - V) + (S + V) = 3.6 + 5.6 \]
This simplifies to:
\[ 2S = 9.2 \]
Thus,
\[ S = \frac{9.2}{2} = 4.6 \text{ km/h} \]

### Step 5: Substitute to Find V
Now, substitute \( S = 4.6 \) back into either equation (1) or (2) to find \( V \). We will use equation (1):
\[ 4.6 - V = 3.6 \]
Rearranging gives:
\[ V = 4.6 - 3.6 = 1 \text{ km/h} \]

### Conclusion
The velocity of the current \( V \) is **1 km/h**.