A person can row a distance of one km upstream in ten minutes and downstream in four minutes. What is the speed of the stream ?

Options

A. 4.5 km/h
B. 4 km/h
C. 9 km/h
D. 5.6 km/h

Answer

To solve the problem, we need to determine the speed of the stream based on the rowing speeds upstream and downstream. Here’s the step-by-step solution:

### Step 1: Convert the time taken for downstream and upstream into hours.
- **Downstream time**: 4 minutes
- **Upstream time**: 10 minutes

To convert minutes into hours, we divide by 60.

**Downstream time in hours**:
\[ \text{Downstream time} = \frac{4 \text{ minutes}}{60} = \frac{1}{15} \text{ hours} \]

**Upstream time in hours**:
\[ \text{Upstream time} = \frac{10 \text{ minutes}}{60} = \frac{1}{6} \text{ hours} \]

### Step 2: Calculate the downstream and upstream speeds.
- **Distance**: 1 km for both upstream and downstream.

**Downstream speed**:
\[ \text{Downstream speed} = \frac{\text{Distance}}{\text{Time}} = \frac{1 \text{ km}}{\frac{1}{15} \text{ hours}} = 1 \times 15 = 15 \text{ km/h} \]

**Upstream speed**:
\[ \text{Upstream speed} = \frac{\text{Distance}}{\text{Time}} = \frac{1 \text{ km}}{\frac{1}{6} \text{ hours}} = 1 \times 6 = 6 \text{ km/h} \]

### Step 3: Use the formula to find the speed of the stream.
The speed of the stream can be calculated using the formula:
\[ \text{Speed of stream} = \frac{\text{Downstream speed} - \text{Upstream speed}}{2} \]

Substituting the values we calculated:
\[ \text{Speed of stream} = \frac{15 \text{ km/h} - 6 \text{ km/h}}{2} = \frac{9 \text{ km/h}}{2} = 4.5 \text{ km/h} \]

### Conclusion
The speed of the stream is **4.5 km/h**.

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