Aman can row12km/h in still water. When the river is running at 2.4km/h,it takes him 1 h to row to a place and to come back. How far is the place?

Answer

To solve the problem, we need to determine how far Aman rows to a place and back, given his rowing speed in still water and the speed of the river current.

### Step-by-Step Solution:

1. **Identify the Given Data**:
- Speed of Aman in still water (S_a) = 12 km/h
- Speed of the river (S_r) = 2.4 km/h
- Total time taken for the round trip (T) = 1 hour

2. **Calculate Effective Speeds**:
- When rowing upstream (against the current), the effective speed of Aman (S_upstream) is:
\[ S_{upstream} = S_a - S_r = 12 \text{ km/h} - 2.4 \text{ km/h} = 9.6 \text{ km/h} \]
- When rowing downstream (with the current), the effective speed of Aman (S_downstream) is:
\[ S_{downstream} = S_a + S_r = 12 \text{ km/h} + 2.4 \text{ km/h} = 14.4 \text{ km/h} \]

3. **Let the Distance to the Place be D**:
- The time taken to row upstream to the place is:
\[ T_{upstream} = \frac{D}{S_{upstream}} = \frac{D}{9.6} \]
- The time taken to row downstream back is:
\[ T_{downstream} = \frac{D}{S_{downstream}} = \frac{D}{14.4} \]

4. **Set Up the Equation**:
- According to the problem, the total time for the round trip is 1 hour:
\[ T_{upstream} + T_{downstream} = 1 \]
- Substituting the expressions for time:
\[ \frac{D}{9.6} + \frac{D}{14.4} = 1 \]

5. **Find a Common Denominator**:
- The least common multiple of 9.6 and 14.4 is 69.12. We can rewrite the equation:
\[ \frac{D \cdot 14.4 + D \cdot 9.6}{9.6 \cdot 14.4} = 1 \]
- This simplifies to:
\[ D(14.4 + 9.6) = 9.6 \cdot 14.4 \]
- Therefore:
\[ D \cdot 24 = 138.24 \]

6. **Solve for D**:
- Now, divide both sides by 24:
\[ D = \frac{138.24}{24} = 5.76 \text{ km} \]

### Conclusion:
The distance to the place is **5.76 km**.