A boat moves downstream at 1 km in 5 minutes and upstream at 1 km in 12 minutes. What is the speed of current?

Options

A. 4.5 km/h
B. 3.5 km/h
C. 2 km/h
D. 2.5 km/h

Answer

To solve the problem, we need to determine the speed of the current based on the given information about the boat's speeds downstream and upstream.

### Step-by-Step Solution:

1. **Define Variables:**
Let the speed of the boat in still water be \( x \) km/h and the speed of the current be \( y \) km/h.

2. **Calculate Downstream Speed:**
The boat moves downstream at 1 km in 5 minutes.
- Convert 5 minutes to hours:
\[ 5 \text{ minutes} = \frac{5}{60} \text{ hours} = \frac{1}{12} \text{ hours} \]
- Speed downstream (distance/time):
\[ \text{Speed downstream} = \frac{1 \text{ km}}{\frac{1}{12} \text{ hours}} = 12 \text{ km/h} \]
- This gives us the equation:
\[ x + y = 12 \quad \text{(Equation 1)} \]

3. **Calculate Upstream Speed:**
The boat moves upstream at 1 km in 12 minutes.
- Convert 12 minutes to hours:
\[ 12 \text{ minutes} = \frac{12}{60} \text{ hours} = \frac{1}{5} \text{ hours} \]
- Speed upstream (distance/time):
\[ \text{Speed upstream} = \frac{1 \text{ km}}{\frac{1}{5} \text{ hours}} = 5 \text{ km/h} \]
- This gives us the equation:
\[ x - y = 5 \quad \text{(Equation 2)} \]

4. **Solve the System of Equations:**
We now have two equations:
- \( x + y = 12 \) (Equation 1)
- \( x - y = 5 \) (Equation 2)

To find \( y \), we can subtract Equation 2 from Equation 1:
\[ (x + y) - (x - y) = 12 - 5 \]
Simplifying this gives:
\[ 2y = 7 \quad \Rightarrow \quad y = \frac{7}{2} = 3.5 \text{ km/h} \]

5. **Conclusion:**
The speed of the current is \( 3.5 \) km/h.