Question

A person rows at \(6\) km/h in still water. It takes him twice the time to row upstream than to row downstream. Find the speed of the stream.

• A. \(2\) km/h
• B. \(3\) km/h
• C. \(4\) km/h
• D. \(1.5\) km/h

Hint:

Remember:

• Upstream speed: \[ b-s \]
• Downstream speed: \[ b+s \]
• For same distance: \[ \text{Time} \propto \frac{1}{\text{Speed}} \]

Answer 1

The Correct Option is B

Concept: For boats and streams: \[ \text{Upstream speed} = b-s \] \[ \text{Downstream speed} = b+s \] where:

• \(b\) = speed of boat in still water
• \(s\) = speed of stream

Also: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Step 1: Write the given information. Speed in still water: \[ b = 6 \text{ km/h} \] Let speed of stream be: \[ s \text{ km/h} \] Thus: \[ \text{Upstream speed} = 6-s \] \[ \text{Downstream speed} = 6+s \]

Step 2: Use the condition on time. Given: \[ \text{Time upstream} = 2 \times \text{Time downstream} \] For equal distances: \[ \frac{1}{6-s} = 2\left(\frac{1}{6+s}\right) \]

Step 3: Solve the equation. \[ \frac{1}{6-s} = \frac{2}{6+s} \] Cross-multiplying: \[ 6+s = 2(6-s) \] \[ 6+s = 12-2s \] \[ 3s = 6 \] \[ s = 2 \] Therefore, \[ \boxed{2 \text{ km/h}} \]