A motor boat whose speed in still water is 18 km/h, takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

Options

A. 6 km/h
B. 8 km/h
C. 10 km/h
D. 12 km/h

Answer

To solve the problem, we need to find the speed of the stream (let's denote it as \( S \)). We know the speed of the motorboat in still water is 18 km/h, and it takes 1 hour longer to go upstream than to return downstream.

### Step-by-Step Solution:

1. **Define Variables:**
- Let the speed of the stream be \( S \) km/h.
- Speed of the motorboat in still water = 18 km/h.

2. **Calculate Speeds:**
- **Upstream Speed:** The speed of the boat going upstream is given by:
\[ \text{Speed upstream} = \text{Speed of boat} - \text{Speed of stream} = 18 - S \text{ km/h} \]
- **Downstream Speed:** The speed of the boat going downstream is given by:
\[ \text{Speed downstream} = \text{Speed of boat} + \text{Speed of stream} = 18 + S \text{ km/h} \]

3. **Calculate Time Taken:**
- **Time taken to go upstream (24 km):**
\[ \text{Time upstream} = \frac{\text{Distance}}{\text{Speed}} = \frac{24}{18 - S} \text{ hours} \]
- **Time taken to go downstream (24 km):**
\[ \text{Time downstream} = \frac{\text{Distance}}{\text{Speed}} = \frac{24}{18 + S} \text{ hours} \]

4. **Set Up the Equation:**
- According to the problem, the time taken to go upstream is 1 hour more than the time taken to go downstream:
\[ \frac{24}{18 - S} = \frac{24}{18 + S} + 1 \]

5. **Clear the Fractions:**
- Multiply through by \( (18 - S)(18 + S) \) to eliminate the denominators:
\[ 24(18 + S) = 24(18 - S) + (18 - S)(18 + S) \]

6. **Expand and Simplify:**
- Expanding both sides:
\[ 432 + 24S = 432 - 24S + (324 - S^2) \]
- Rearranging gives:
\[ 24S + 24S + S^2 = 324 \]
\[ S^2 + 48S - 324 = 0 \]

7. **Solve the Quadratic Equation:**
- We can factor or use the quadratic formula. Factoring gives:
\[ (S + 54)(S - 6) = 0 \]
- Thus, \( S = -54 \) or \( S = 6 \). Since speed cannot be negative, we take:
\[ S = 6 \text{ km/h} \]

### Final Answer:
The speed of the stream is **6 km/h**.