A man rows a boat 18 kilometres in 4 hours down - stream and returns upstream in 12 hours . The speed of the stram (in km per hour) is :

Options

A. 1
B. 1.5
C. 2
D. 1.75

Answer

To solve the problem step by step, we will determine the speed of the boat in still water and the speed of the stream based on the information provided.

### Step 1: Understand the Problem
We know:
- Distance downstream = 18 km
- Time taken downstream = 4 hours
- Time taken upstream = 12 hours

### Step 2: Calculate Downstream Speed
The speed downstream (S_d) can be calculated using the formula:
\[ S_d = \frac{\text{Distance}}{\text{Time}} \]
Substituting the values:
\[ S_d = \frac{18 \text{ km}}{4 \text{ hours}} = 4.5 \text{ km/h} \]

### Step 3: Calculate Upstream Speed
The speed upstream (S_u) can also be calculated using the same formula:
\[ S_u = \frac{\text{Distance}}{\text{Time}} \]
Substituting the values:
\[ S_u = \frac{18 \text{ km}}{12 \text{ hours}} = 1.5 \text{ km/h} \]

### Step 4: Set Up the Equations
Let:
- Speed of the boat in still water = \( a \) km/h
- Speed of the stream = \( b \) km/h

From the information given, we can set up the following equations:
1. Downstream: \( a + b = 4.5 \) (1)
2. Upstream: \( a - b = 1.5 \) (2)

### Step 5: Solve the Equations
Now we can solve these two equations simultaneously.

**Adding equations (1) and (2):**
\[ (a + b) + (a - b) = 4.5 + 1.5 \]
\[ 2a = 6 \implies a = 3 \text{ km/h} \]

**Substituting \( a \) back into equation (1):**
\[ 3 + b = 4.5 \implies b = 4.5 - 3 = 1.5 \text{ km/h} \]

### Conclusion
The speed of the stream (b) is **1.5 km/h**.

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