The river flows at 4 km/h. A boat can go downstream thrice as fast as upstream The speed of boat in still water is

Options

A. 12 km/h
B. 16 km/h
C. 8 km/h
D. 10 km/h

Answer

To solve the problem, we need to find the speed of the boat in still water given the conditions of the river's flow and the boat's speed both upstream and downstream.

### Step-by-Step Solution:

1. **Define Variables:**
Let the speed of the boat in still water be \( x \) km/h.

2. **Determine Upstream and Downstream Speeds:**
- The speed of the river is given as 4 km/h.
- Therefore, the speed of the boat upstream (against the current) is:
\[ \text{Upstream speed} = x - 4 \text{ km/h} \]
- The speed of the boat downstream (with the current) is:
\[ \text{Downstream speed} = x + 4 \text{ km/h} \]

3. **Set Up the Equation:**
According to the problem, the speed of the boat downstream is three times the speed of the boat upstream:
\[ x + 4 = 3(x - 4) \]

4. **Expand and Simplify the Equation:**
Expanding the right side of the equation:
\[ x + 4 = 3x - 12 \]
Now, rearranging the equation to isolate \( x \):
\[ 4 + 12 = 3x - x \]
\[ 16 = 2x \]

5. **Solve for \( x \):**
Dividing both sides by 2 gives:
\[ x = 8 \text{ km/h} \]

6. **Conclusion:**
The speed of the boat in still water is \( 8 \) km/h.