A man can row upstream at 10 km/hr and downstream at 16 km/hr. Find the speed of man in still water?

Answer

To find the speed of the man in still water, we can follow these steps:

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

### Step 2: Set Up Equations
From the problem, we know:
- The speed of the man rowing upstream (against the current) is given as 10 km/hr. This can be expressed as:
\[ x - y = 10 \quad \text{(1)} \]
- The speed of the man rowing downstream (with the current) is given as 16 km/hr. This can be expressed as:
\[ x + y = 16 \quad \text{(2)} \]

### Step 3: Solve the Equations
Now, we can solve these two equations simultaneously.

#### Adding the two equations:
\[ (x - y) + (x + y) = 10 + 16 \]
This simplifies to:
\[ 2x = 26 \]

#### Step 4: Isolate \( x \)
Now, divide both sides by 2:
\[ x = \frac{26}{2} = 13 \text{ km/hr} \]

### Conclusion
The speed of the man in still water is:
\[ \boxed{13 \text{ km/hr}} \]

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