Finding Speed of Boat and Stream

Video Explanation

Question

Ritu can row downstream 20 km in 2 hours and upstream 4 km in 2 hours. Find her speed in still water and the speed of the current.

Solution

Step 1: Concept

Speed = Distance / Time

Step 2: Let Variables

Let speed in still water = \(x\) km/h

Let speed of current = \(y\) km/h

Downstream speed = \(x + y\), Upstream speed = \(x – y\)

Step 3: Form Equations

Downstream:

\[ x + y = \frac{20}{2} = 10 \quad (1) \]

Upstream:

\[ x – y = \frac{4}{2} = 2 \quad (2) \]

Step 4: Solve Linear Equations

Add:

\[ 2x = 12 \Rightarrow x = 6 \]

Substitute:

\[ 6 + y = 10 \Rightarrow y = 4 \]

Conclusion

\[ \text{Speed in still water} = 6 \text{ km/h}, \quad \text{Speed of current} = 4 \text{ km/h} \]

Verification

Downstream speed = \(6 + 4 = 10\) → time = \(20/10 = 2\) ✔

Upstream speed = \(6 – 4 = 2\) → time = \(4/2 = 2\) ✔