A boat goes 12 km in 1 h in still water. It takes thrice time in covering the same distance against the current. Find the speed of the current.

Options

A. a. 8 km/h
B. b. 12 km/h
C. c. 6 km/h
D. d. 7 km/h

Answer

To solve the problem step by step, we will use the information provided in the question regarding the speed of the boat in still water and the time taken to cover the distance against the current.

### Step 1: Identify the speed of the boat in still water
The speed of the boat in still water is given as 12 km/h.

### Step 2: Determine the time taken to cover the distance against the current
The boat takes thrice the time to cover the same distance against the current. If it takes 1 hour to cover 12 km in still water, then against the current, it takes:
\[ \text{Time against current} = 3 \times \text{Time in still water} = 3 \times 1 \text{ hour} = 3 \text{ hours} \]

### Step 3: Calculate the effective speed against the current
The distance covered against the current is still 12 km, and the time taken is 3 hours. Therefore, the effective speed against the current can be calculated as:
\[ \text{Speed against current} = \frac{\text{Distance}}{\text{Time}} = \frac{12 \text{ km}}{3 \text{ hours}} = 4 \text{ km/h} \]

### Step 4: Set up the equation for the speed of the current
Let the speed of the current be \( x \) km/h. The effective speed against the current is given by the formula:
\[ \text{Speed against current} = \text{Speed in still water} - \text{Speed of current} \]
Substituting the known values:
\[ 4 \text{ km/h} = 12 \text{ km/h} - x \]

### Step 5: Solve for the speed of the current
Rearranging the equation to solve for \( x \):
\[ x = 12 \text{ km/h} - 4 \text{ km/h} \]
\[ x = 8 \text{ km/h} \]

### Conclusion
The speed of the current is **8 km/h**.

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