A boat can travel 9.6 km downstream in 36 min . If speed of the water current is 10% of the speed of the boat in downstream . How much time will boat take to travel 38.4 km upstream .

Options

A. 2 hours
B. 3 hours
C. 1.25 hours
D. 1.5 hours

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the downstream speed of the boat
The boat travels 9.6 km downstream in 36 minutes. First, we need to convert the time from minutes to hours.

\[ \text{Time in hours} = \frac{36 \text{ minutes}}{60} = 0.6 \text{ hours} \]

Now, we can calculate the downstream speed:

\[ \text{Downstream speed} = \frac{\text{Distance}}{\text{Time}} = \frac{9.6 \text{ km}}{0.6 \text{ hours}} = 16 \text{ km/h} \]

### Step 2: Determine the speed of the water current
The speed of the water current is given as 10% of the speed of the boat in downstream.

\[ \text{Speed of current} = 10\% \text{ of } 16 \text{ km/h} = \frac{10}{100} \times 16 = 1.6 \text{ km/h} \]

### Step 3: Calculate the speed of the boat in still water
Let the speed of the boat in still water be \( x \) km/h. The downstream speed is the sum of the speed of the boat in still water and the speed of the current:

\[ \text{Downstream speed} = x + \text{Speed of current} \]

Substituting the known values:

\[ 16 = x + 1.6 \]

Now, solve for \( x \):

\[ x = 16 - 1.6 = 14.4 \text{ km/h} \]

### Step 4: Calculate the upstream speed of the boat
The upstream speed is the speed of the boat in still water minus the speed of the current:

\[ \text{Upstream speed} = x - \text{Speed of current} = 14.4 - 1.6 = 12.8 \text{ km/h} \]

### Step 5: Calculate the time taken to travel 38.4 km upstream
To find the time taken to travel 38.4 km upstream, we use the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the values:

\[ \text{Time} = \frac{38.4 \text{ km}}{12.8 \text{ km/h}} = 3 \text{ hours} \]

### Final Answer
The boat will take **3 hours** to travel 38.4 km upstream.

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