Speed of a boat in still water is 12 km/h and that of the current is 3 km/h. A man rows a boat upstream up to 135 km and returns downstream to the starting point. Find the total time taken for the entire journey in hours.

Options

A. 24
B. 48
C. 36
D. 30

Answer

To solve the problem step by step, we will calculate the time taken for both upstream and downstream journeys separately and then sum them up to find the total time taken for the entire journey.

### Step 1: Determine the speed of the boat upstream
The speed of the boat in still water is given as 12 km/h, and the speed of the current is 3 km/h. To find the speed of the boat while rowing upstream, we subtract the speed of the current from the speed of the boat in still water.

**Calculation:**
\[ \text{Speed upstream} = \text{Speed of boat in still water} - \text{Speed of current} = 12 \text{ km/h} - 3 \text{ km/h} = 9 \text{ km/h} \]

### Step 2: Calculate the time taken to row upstream
The distance traveled upstream is given as 135 km. We can find the time taken to row upstream using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

**Calculation:**
\[ T_1 = \frac{135 \text{ km}}{9 \text{ km/h}} = 15 \text{ hours} \]

### Step 3: Determine the speed of the boat downstream
To find the speed of the boat while rowing downstream, we add the speed of the current to the speed of the boat in still water.

**Calculation:**
\[ \text{Speed downstream} = \text{Speed of boat in still water} + \text{Speed of current} = 12 \text{ km/h} + 3 \text{ km/h} = 15 \text{ km/h} \]

### Step 4: Calculate the time taken to row downstream
Using the same formula for time, we can find the time taken to row downstream.

**Calculation:**
\[ T_2 = \frac{135 \text{ km}}{15 \text{ km/h}} = 9 \text{ hours} \]

### Step 5: Calculate the total time for the entire journey
Now, we can find the total time taken for the entire journey by adding the time taken for both upstream and downstream.

**Calculation:**
\[ \text{Total Time} = T_1 + T_2 = 15 \text{ hours} + 9 \text{ hours} = 24 \text{ hours} \]

### Final Answer
The total time taken for the entire journey is **24 hours**.

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