A man takes 3 hours 45 minutes to row a boat 15 km downstream of a river and 2 hours 30 minutes to cover a distance of 5 km upstream. Find the speed of the current.

Options

A. 1kmph
B. 3kmph
C. 5kmph
D. 2kmph

Answer

To solve the problem of finding the speed of the current, we will follow these steps:

### Step-by-Step Solution:

1. **Convert Time to Hours**:
- The time taken to row downstream is 3 hours 45 minutes.
- Convert this to hours:
\[ 3 \text{ hours} + \frac{45 \text{ minutes}}{60} = 3 + 0.75 = 3.75 \text{ hours} \]
- The time taken to row upstream is 2 hours 30 minutes.
- Convert this to hours:
\[ 2 \text{ hours} + \frac{30 \text{ minutes}}{60} = 2 + 0.5 = 2.5 \text{ hours} \]

2. **Calculate Speed Downstream**:
- The distance covered downstream is 15 km.
- Speed is calculated as:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{15 \text{ km}}{3.75 \text{ hours}} = 4 \text{ km/h} \]
- Let the speed of the man in still water be \( x \) km/h and the speed of the current be \( y \) km/h.
- Therefore, the equation for downstream is:
\[ x + y = 4 \quad \text{(1)} \]

3. **Calculate Speed Upstream**:
- The distance covered upstream is 5 km.
- Speed is calculated as:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{5 \text{ km}}{2.5 \text{ hours}} = 2 \text{ km/h} \]
- The equation for upstream is:
\[ x - y = 2 \quad \text{(2)} \]

4. **Solve the Equations**:
- We have two equations:
1. \( x + y = 4 \)
2. \( x - y = 2 \)
- To solve these equations, we can add them:
\[ (x + y) + (x - y) = 4 + 2 \]
\[ 2x = 6 \implies x = 3 \text{ km/h} \]
- Now substitute \( x \) back into one of the equations to find \( y \):
\[ 3 + y = 4 \implies y = 1 \text{ km/h} \]

5. **Conclusion**:
- The speed of the current \( y \) is **1 km/h**.