A boat moves downstream at the rate of 1 km in 6 min and upstream at the rate of 1 km in 10 min. The speed of the current (in km/hr) is

Options

A. 1
B. 1.5
C. 2
D. 2.5

Answer

To solve the problem, we need to find the speed of the current based on the downstream and upstream speeds of the boat.

### Step 1: Convert the times into hours
- The boat moves downstream at 1 km in 6 minutes.
- To convert minutes into hours:
\[ 6 \text{ minutes} = \frac{6}{60} \text{ hours} = 0.1 \text{ hours} \]
- The boat moves upstream at 1 km in 10 minutes.
- To convert minutes into hours:
\[ 10 \text{ minutes} = \frac{10}{60} \text{ hours} = \frac{1}{6} \text{ hours} \approx 0.1667 \text{ hours} \]

### Step 2: Calculate the speeds downstream and upstream
- Downstream speed (Speed with the current):
\[ \text{Speed}_{\text{down}} = \frac{\text{Distance}}{\text{Time}} = \frac{1 \text{ km}}{0.1 \text{ hours}} = 10 \text{ km/hr} \]
- Upstream speed (Speed against the current):
\[ \text{Speed}_{\text{up}} = \frac{\text{Distance}}{\text{Time}} = \frac{1 \text{ km}}{\frac{1}{6} \text{ hours}} = 6 \text{ km/hr} \]

### Step 3: Set up the equations for speed
Let the speed of the boat in still water be \( b \) km/hr and the speed of the current be \( c \) km/hr.
- From the downstream speed:
\[ b + c = 10 \quad \text{(1)} \]
- From the upstream speed:
\[ b - c = 6 \quad \text{(2)} \]

### Step 4: Solve the equations
- Add equations (1) and (2):
\[ (b + c) + (b - c) = 10 + 6 \]
\[ 2b = 16 \implies b = 8 \text{ km/hr} \]

- Substitute \( b \) back into equation (1):
\[ 8 + c = 10 \implies c = 10 - 8 = 2 \text{ km/hr} \]

### Conclusion
The speed of the current is \( 2 \text{ km/hr} \).