Length of river is 40 km. Speed of stream is 3 km/h. Boat takes 6 hours more to return than to go in river. Find the speed of boat in still water.

Answer

To solve the problem, we need to find the speed of the boat in still water (let's denote it as \( x \) km/h). We know the following:

1. Length of the river = 40 km
2. Speed of the stream = 3 km/h
3. The boat takes 6 hours more to return upstream than to go downstream.

### Step 1: Define the speeds
- Speed of the boat downstream (with the current) = \( x + 3 \) km/h
- Speed of the boat upstream (against the current) = \( x - 3 \) km/h

### Step 2: Set up the time equations
- Time taken to go downstream = Distance / Speed = \( \frac{40}{x + 3} \)
- Time taken to go upstream = Distance / Speed = \( \frac{40}{x - 3} \)

According to the problem, the time taken to return upstream is 6 hours more than the time taken to go downstream:
\[ \frac{40}{x - 3} = \frac{40}{x + 3} + 6 \]

### Step 3: Solve the equation
1. Rearranging the equation:
\[ \frac{40}{x - 3} - \frac{40}{x + 3} = 6 \]

2. Finding a common denominator:
\[ \frac{40(x + 3) - 40(x - 3)}{(x - 3)(x + 3)} = 6 \]

3. Simplifying the numerator:
\[ \frac{40x + 120 - 40x + 120}{(x - 3)(x + 3)} = 6 \]
\[ \frac{240}{(x - 3)(x + 3)} = 6 \]

4. Cross-multiplying to eliminate the fraction:
\[ 240 = 6(x^2 - 9) \]
\[ 240 = 6x^2 - 54 \]

5. Rearranging the equation:
\[ 6x^2 - 54 - 240 = 0 \]
\[ 6x^2 - 294 = 0 \]
\[ x^2 = 49 \]

6. Taking the square root:
\[ x = 7 \quad (\text{since speed cannot be negative}) \]

### Conclusion
The speed of the boat in still water is **7 km/h**.