A person car row with the stream at 8 km/h and against the stream at 6 km/h. The speed of the current in km/h is

Options

A. 1
B. 2
C. 4
D. 5

Answer

To solve the problem of finding the speed of the current when a person rows with the stream and against the stream, we can follow these steps:

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

### Step 2: Set Up Equations
From the problem, we have two scenarios:
1. **With the stream**: The effective speed is the sum of the person's speed and the current's speed.
\[ V + V_d = 8 \quad \text{(Equation 1)} \]
2. **Against the stream**: The effective speed is the difference between the person's speed and the current's speed.
\[ V - V_d = 6 \quad \text{(Equation 2)} \]

### Step 3: Solve the Equations
Now, we can solve these two equations simultaneously.

#### Step 3.1: Add Equation 1 and Equation 2
\[ (V + V_d) + (V - V_d) = 8 + 6 \]
This simplifies to:
\[ 2V = 14 \]
So,
\[ V = 7 \quad \text{(speed of the person in still water)} \]

#### Step 3.2: Substitute \( V \) back into Equation 1
Now, substitute \( V = 7 \) into Equation 1 to find \( V_d \):
\[ 7 + V_d = 8 \]
This simplifies to:
\[ V_d = 8 - 7 = 1 \]

### Conclusion
The speed of the current is \( 1 \) km/h.