A boatman rows 1 km in 5 min along the stream and 6 km in 1 h against the stream. The speed of the stream is

Options

A. 3 km/h
B. 6 km/h
C. 10 km/h
D. 12 km/h

Answer

To solve the problem of finding the speed of the stream based on the given rowing speeds of the boatman, we can follow these steps:

### Step 1: Identify the given data
- The boatman rows 1 km in 5 minutes along the stream.
- The boatman rows 6 km in 1 hour against the stream.

### Step 2: Convert the downstream speed to km/h
- Downstream speed is given as 1 km in 5 minutes.
- To convert this to kilometers per hour, we need to find out how far the boat travels in 60 minutes.

\[ \text{Downstream speed} = \frac{1 \text{ km}}{5 \text{ min}} \times \frac{60 \text{ min}}{1 \text{ hour}} = \frac{1 \times 60}{5} = 12 \text{ km/h} \]

### Step 3: Identify the upstream speed
- The upstream speed is given as 6 km in 1 hour.

\[ \text{Upstream speed} = 6 \text{ km/h} \]

### Step 4: Use the formula to find the speed of the stream
- The speed of the stream can be calculated using the formula:

\[ \text{Speed of the stream} = \frac{\text{Downstream speed} - \text{Upstream speed}}{2} \]

- Substitute the values we found:

\[ \text{Speed of the stream} = \frac{12 \text{ km/h} - 6 \text{ km/h}}{2} = \frac{6 \text{ km/h}}{2} = 3 \text{ km/h} \]

### Final Answer
The speed of the stream is **3 km/h**.

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