A boat covers a distance of 14 km in 4 hours along the flow. What is the speed of the boat in still water, if the speed of the flow of water is 2 km/h?

Options

A. 2 km/hr
B. 3 km/hr
C. 2.5 km/hr
D. 1.5 km/hr

Answer

To solve the problem step by step, let's break it down.

### Step 1: Determine the speed of the boat downstream
The boat covers a distance of 14 km in 4 hours. To find the speed of the boat downstream, we use the formula:

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

Substituting the values:

\[ \text{Speed} = \frac{14 \text{ km}}{4 \text{ hours}} = 3.5 \text{ km/h} \]

### Step 2: Set up the equation for the speed of the boat in still water
Let the speed of the boat in still water be \( x \) km/h. The speed of the flow of water is given as 2 km/h. Therefore, the speed of the boat downstream (speed in still water + speed of the flow) can be expressed as:

\[ \text{Speed downstream} = x + 2 \text{ km/h} \]

### Step 3: Create the equation
We know from Step 1 that the speed downstream is 3.5 km/h. Thus, we can set up the equation:

\[ x + 2 = 3.5 \]

### Step 4: Solve for \( x \)
To find \( x \), we rearrange the equation:

\[ x = 3.5 - 2 \]

Calculating this gives:

\[ x = 1.5 \text{ km/h} \]

### Conclusion
The speed of the boat in still water is 1.5 km/h.

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