A boat travels upstream from B to A and downstream from A to B in 3 hrs. If the speed of the boat in still water is 9 km/hr and the speed of the current is 3 km/hr, the distance between A and B is:

Options

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

Answer

To solve the problem, we need to find the distance between points A and B given the time taken for the boat to travel upstream and downstream, as well as the speeds of the boat in still water and the current.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Speed of the boat in still water (B) = 9 km/hr
- Speed of the current (C) = 3 km/hr
- Total time for the journey (upstream + downstream) = 3 hours

2. **Calculate Effective Speeds:**
- **Upstream Speed (U)**: This is the speed of the boat against the current.
\[ U = B - C = 9 \text{ km/hr} - 3 \text{ km/hr} = 6 \text{ km/hr} \]
- **Downstream Speed (D)**: This is the speed of the boat with the current.
\[ D = B + C = 9 \text{ km/hr} + 3 \text{ km/hr} = 12 \text{ km/hr} \]

3. **Let Distance Between A and B be D km:**
- Time taken to travel upstream from B to A:
\[ \text{Time}_{\text{upstream}} = \frac{D}{U} = \frac{D}{6} \]
- Time taken to travel downstream from A to B:
\[ \text{Time}_{\text{downstream}} = \frac{D}{D} = \frac{D}{12} \]

4. **Set Up the Equation:**
- The total time for the journey is given as 3 hours:
\[ \frac{D}{6} + \frac{D}{12} = 3 \]

5. **Find a Common Denominator:**
- The common denominator for 6 and 12 is 12. Rewrite the equation:
\[ \frac{2D}{12} + \frac{D}{12} = 3 \]
- Combine the fractions:
\[ \frac{3D}{12} = 3 \]

6. **Solve for D:**
- Multiply both sides by 12:
\[ 3D = 36 \]
- Divide by 3:
\[ D = 12 \text{ km} \]

### Final Answer:
The distance between A and B is **12 km**.

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