A man can go 30km/hr upstream & 34 km/h downstream. Find the speed of current & speed of man in still water.

Answer

To solve the problem, we need to find the speed of the current (let's denote it as \( A \)) and the speed of the man in still water (denote it as \( B \)). We are given the following information:

- Speed upstream = 30 km/h
- Speed downstream = 34 km/h

### Step 1: Set up the equations
We know that:
- The speed of the man in still water \( B \) plus the speed of the current \( A \) gives the downstream speed:
\[ B + A = 34 \quad \text{(1)} \]
- The speed of the man in still water \( B \) minus the speed of the current \( A \) gives the upstream speed:
\[ B - A = 30 \quad \text{(2)} \]

### Step 2: Solve the equations
Now, we can add equations (1) and (2) to eliminate \( A \):
\[ (B + A) + (B - A) = 34 + 30 \]
This simplifies to:
\[ 2B = 64 \]
Now, divide both sides by 2:
\[ B = 32 \quad \text{(Speed of man in still water)} \]

### Step 3: Find the speed of the current
Now that we have \( B \), we can substitute it back into either equation (1) or (2) to find \( A \). Let's use equation (1):
\[ 32 + A = 34 \]
Subtract 32 from both sides:
\[ A = 2 \quad \text{(Speed of current)} \]

### Final Answers
- Speed of the man in still water \( B = 32 \) km/h
- Speed of the current \( A = 2 \) km/h