A boat running downstream covers a distance of 20 km in 2 hrd while it covers the same distance uptream in 5 hrd .Then speed of the boat in still water is

Options

A. 7km /hr
B. 8km/hr
C. 9km/hr
D. 10 km /hr

Answer

To find the speed of the boat in still water, we can follow these steps:

### Step 1: Determine the speed downstream and upstream
- **Downstream speed**: The boat covers 20 km in 2 hours.
\[ \text{Speed downstream} = \frac{\text{Distance}}{\text{Time}} = \frac{20 \text{ km}}{2 \text{ hr}} = 10 \text{ km/hr} \]

- **Upstream speed**: The boat covers the same distance of 20 km in 5 hours.
\[ \text{Speed upstream} = \frac{\text{Distance}}{\text{Time}} = \frac{20 \text{ km}}{5 \text{ hr}} = 4 \text{ km/hr} \]

### Step 2: Set up equations for the speeds
Let:
- \( x \) = speed of the boat in still water (km/hr)
- \( y \) = speed of the current (km/hr)

From the information given:
1. Downstream speed: \( x + y = 10 \) (Equation 1)
2. Upstream speed: \( x - y = 4 \) (Equation 2)

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

- From Equation 1:
\[ x + y = 10 \quad \text{(1)} \]

- From Equation 2:
\[ x - y = 4 \quad \text{(2)} \]

### Step 4: Add the two equations
Adding Equation 1 and Equation 2:
\[ (x + y) + (x - y) = 10 + 4 \]
This simplifies to:
\[ 2x = 14 \]
Thus, solving for \( x \):
\[ x = \frac{14}{2} = 7 \text{ km/hr} \]

### Step 5: Conclusion
The speed of the boat in still water is:
\[ \text{Speed of the boat in still water} = 7 \text{ km/hr} \]

---