A man rows upstream 16 km and downstream 28 km taking 5 hours each time. The velocity of the current is -----

Options

A. 2.4 km/hr
B. 1.2 km/hr
C. 3.6 km/hr
D. 1.8 km/hr

Answer

To solve the problem, we will follow these steps:

### Step 1: Define Variables
Let:
- \( x \) = speed of the man in still water (in km/h)
- \( y \) = speed of the current (in km/h)

### Step 2: Determine Upstream and Downstream Velocities
The effective speed while rowing upstream (against the current) is given by:
\[ \text{Upstream speed} (v) = x - y \]
The effective speed while rowing downstream (with the current) is given by:
\[ \text{Downstream speed} (u) = x + y \]

### Step 3: Calculate Speeds from Given Distances and Times
We know that:
- Distance upstream = 16 km, Time = 5 hours
- Distance downstream = 28 km, Time = 5 hours

Using the formula \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \):
1. For upstream:
\[ v = \frac{16 \text{ km}}{5 \text{ hours}} = 3.2 \text{ km/h} \]
2. For downstream:
\[ u = \frac{28 \text{ km}}{5 \text{ hours}} = 5.6 \text{ km/h} \]

### Step 4: Set Up Equations
From the equations for upstream and downstream speeds:
1. \( v = x - y = 3.2 \)
2. \( u = x + y = 5.6 \)

### Step 5: Solve the System of Equations
We can solve these two equations simultaneously:
1. From \( x - y = 3.2 \) (Equation 1)
2. From \( x + y = 5.6 \) (Equation 2)

Adding both equations:
\[ (x - y) + (x + y) = 3.2 + 5.6 \]
\[ 2x = 8.8 \implies x = 4.4 \text{ km/h} \]

Now, substituting \( x \) back into either equation to find \( y \):
Using Equation 1:
\[ 4.4 - y = 3.2 \implies y = 4.4 - 3.2 = 1.2 \text{ km/h} \]

### Step 6: Conclusion
The velocity of the current \( y \) is:
\[ \boxed{1.2 \text{ km/h}} \]