A boat moves downstream at 1 km in 5 min and upstream at 1 km in 12 min what is the speed of the 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 find the speed of the current based on the downstream and upstream speeds of the boat.

### Step-by-Step Solution:

1. **Convert Time to Hours:**
- The boat moves downstream at 1 km in 5 minutes.
- Convert 5 minutes to hours:
\[ 5 \text{ minutes} = \frac{5}{60} \text{ hours} = \frac{1}{12} \text{ hours} \]
- The boat moves upstream at 1 km in 12 minutes.
- Convert 12 minutes to hours:
\[ 12 \text{ minutes} = \frac{12}{60} \text{ hours} = \frac{1}{5} \text{ hours} \]

2. **Calculate Downstream Speed:**
- Speed is given by the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
- For downstream:
\[ \text{Downstream Speed} = \frac{1 \text{ km}}{\frac{1}{12} \text{ hours}} = 1 \times 12 = 12 \text{ km/h} \]

3. **Calculate Upstream Speed:**
- For upstream:
\[ \text{Upstream Speed} = \frac{1 \text{ km}}{\frac{1}{5} \text{ hours}} = 1 \times 5 = 5 \text{ km/h} \]

4. **Set Up the Equations:**
- Let \( B \) be the speed of the boat in still water and \( W \) be the speed of the current.
- The downstream speed can be expressed as:
\[ B + W = 12 \text{ km/h} \]
- The upstream speed can be expressed as:
\[ B - W = 5 \text{ km/h} \]

5. **Solve the Equations:**
- We have the two equations:
1. \( B + W = 12 \)
2. \( B - W = 5 \)
- Add the two equations:
\[ (B + W) + (B - W) = 12 + 5 \]
\[ 2B = 17 \quad \Rightarrow \quad B = \frac{17}{2} = 8.5 \text{ km/h} \]
- Now substitute \( B \) back into one of the equations to find \( W \):
\[ 8.5 + W = 12 \quad \Rightarrow \quad W = 12 - 8.5 = 3.5 \text{ km/h} \]

6. **Conclusion:**
- The speed of the current is \( 3.5 \text{ km/h} \).