A motor boat takes 2 hours to travel a distance of 9 km downstream and it takes 6 hours tomtravel the same distance against the current.The speed of the boat in still water and that of the current (in km/h) respectively are:

Options

A. 6,5
B. 3,1.5
C. 8,5
D. 9,3

Answer

To solve the problem step by step, we need to find the speed of the boat in still water (B) and the speed of the current (W).

### Step 1: Understand the problem
We know that:
- Distance downstream = 9 km, Time taken = 2 hours
- Distance upstream = 9 km, Time taken = 6 hours

### Step 2: Calculate the speeds downstream and upstream
Using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

**Downstream speed (B + W)**:
\[ \text{Speed}_{\text{downstream}} = \frac{9 \text{ km}}{2 \text{ hours}} = 4.5 \text{ km/h} \]
So,
\[ B + W = 4.5 \text{ km/h} \] (Equation 1)

**Upstream speed (B - W)**:
\[ \text{Speed}_{\text{upstream}} = \frac{9 \text{ km}}{6 \text{ hours}} = 1.5 \text{ km/h} \]
So,
\[ B - W = 1.5 \text{ km/h} \] (Equation 2)

### Step 3: Set up the equations
Now we have two equations:
1. \( B + W = 4.5 \)
2. \( B - W = 1.5 \)

### Step 4: Solve the equations
To find B and W, we can add both equations together:
\[ (B + W) + (B - W) = 4.5 + 1.5 \]
This simplifies to:
\[ 2B = 6 \]
So,
\[ B = \frac{6}{2} = 3 \text{ km/h} \]

### Step 5: Substitute B back to find W
Now substitute B back into one of the equations to find W. Using Equation 1:
\[ 3 + W = 4.5 \]
This simplifies to:
\[ W = 4.5 - 3 = 1.5 \text{ km/h} \]

### Final Answer
Thus, the speed of the boat in still water (B) is **3 km/h**, and the speed of the current (W) is **1.5 km/h**.