Formulate the following problems as a pair of equations, and hence find their solutions:
Ritu can row downstream 20 km in 2 hours, and upstream 4km in 2 hours. Find her speed of rowing in still water and the speed of the current.

Answer

To solve the problem, we need to formulate a pair of equations based on the information given about Ritu's rowing downstream and upstream.

### Step 1: Define Variables
Let:
- \( r \) = speed of Ritu in still water (in km/h)
- \( c \) = speed of the current (in km/h)

### Step 2: Determine Speeds
From the problem, we know:
1. Ritu rows downstream 20 km in 2 hours.
2. Ritu rows upstream 4 km in 2 hours.

We can calculate her speeds downstream and upstream:
- **Downstream speed** = Distance / Time = \( \frac{20 \text{ km}}{2 \text{ hours}} = 10 \text{ km/h} \)
- **Upstream speed** = Distance / Time = \( \frac{4 \text{ km}}{2 \text{ hours}} = 2 \text{ km/h} \)

### Step 3: Formulate Equations
The relationship between the speeds can be expressed as:
- Downstream speed = Speed in still water + Speed of current
- Upstream speed = Speed in still water - Speed of current

This gives us the following equations:
1. \( r + c = 10 \) (Equation 1)
2. \( r - c = 2 \) (Equation 2)

### Step 4: Solve the Equations
Now, we can solve these equations simultaneously.

**Adding Equation 1 and Equation 2:**
\[ (r + c) + (r - c) = 10 + 2 \]
\[ 2r = 12 \]
\[ r = 6 \text{ km/h} \]

**Substituting \( r \) back into Equation 1:**
\[ 6 + c = 10 \]
\[ c = 10 - 6 = 4 \text{ km/h} \]

### Step 5: Conclusion
Thus, Ritu's speed in still water is \( 6 \text{ km/h} \) and the speed of the current is \( 4 \text{ km/h} \).

### Summary of Results
- Speed of rowing in still water, \( r = 6 \text{ km/h} \)
- Speed of the current, \( c = 4 \text{ km/h} \)

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