A motor boat takes 2 hours to travel a distance of 9 km downstream and it takes 6 hours to travel the same distance against the current. The speed of the boat is 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, we need to find the speed of the motorboat in still water (let's denote it as \( x \) km/h) and the speed of the current (denote it as \( y \) km/h).

### Step-by-Step Solution:

1. **Determine Downstream Speed:**
- The motorboat takes 2 hours to travel 9 km downstream.
- Downstream speed can be calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{9 \text{ km}}{2 \text{ hours}} = 4.5 \text{ km/h} \]
- The downstream speed is also expressed as \( x + y \) (speed of the boat plus speed of the current).

**Hint:** Use the formula for speed (Distance/Time) to find the downstream speed.

2. **Determine Upstream Speed:**
- The motorboat takes 6 hours to travel the same distance of 9 km upstream.
- Upstream speed can be calculated as:
\[ \text{Speed} = \frac{9 \text{ km}}{6 \text{ hours}} = 1.5 \text{ km/h} \]
- The upstream speed is expressed as \( x - y \) (speed of the boat minus speed of the current).

**Hint:** Again, apply the speed formula to find the upstream speed.

3. **Set Up the Equations:**
- From the downstream speed, we have:
\[ x + y = 4.5 \quad \text{(Equation 1)} \]
- From the upstream speed, we have:
\[ x - y = 1.5 \quad \text{(Equation 2)} \]

**Hint:** Write down the equations based on the speeds calculated in the previous steps.

4. **Solve the Equations:**
- Add Equation 1 and Equation 2:
\[ (x + y) + (x - y) = 4.5 + 1.5 \]
\[ 2x = 6 \quad \Rightarrow \quad x = 3 \text{ km/h} \]

**Hint:** Adding the equations helps eliminate \( y \) and solve for \( x \).

5. **Find the Speed of the Current:**
- Substitute \( x = 3 \) back into Equation 1:
\[ 3 + y = 4.5 \]
\[ y = 4.5 - 3 = 1.5 \text{ km/h} \]

**Hint:** Substitute the value of \( x \) into one of the original equations to find \( y \).

### Final Answer:
- The speed of the boat in still water is \( 3 \) km/h and the speed of the current is \( 1.5 \) km/h.