A boat moves upstream at the rate of 1 km in 10 minutes and downstream at the rate of 1 km in 6 minutes. The speed of the current is -----

Options

A. 1 km/hr
B. 1.5 km/hr
C. 2 km/hr
D. 2.5 km/hr

Answer

To find the speed of the current, we will follow these steps:

### Step 1: Calculate the downstream speed
The boat moves downstream at the rate of 1 km in 6 minutes. To convert this speed to km/h, we can use the following calculation:

\[ \text{Downstream speed} = \frac{1 \text{ km}}{6 \text{ minutes}} \times \frac{60 \text{ minutes}}{1 \text{ hour}} = 10 \text{ km/h} \]

### Step 2: Calculate the upstream speed
The boat moves upstream at the rate of 1 km in 10 minutes. Similarly, we convert this speed to km/h:

\[ \text{Upstream speed} = \frac{1 \text{ km}}{10 \text{ minutes}} \times \frac{60 \text{ minutes}}{1 \text{ hour}} = 6 \text{ km/h} \]

### Step 3: Use the formula to find the speed of the current
The speed of the current can be calculated using the formula:

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

Substituting the values we found:

\[ \text{Speed of current} = \frac{10 \text{ km/h} - 6 \text{ km/h}}{2} = \frac{4 \text{ km/h}}{2} = 2 \text{ km/h} \]

### Conclusion
The speed of the current is **2 km/h**.

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