Question

A diver rowing at the speed of 3 km/h in still water takes double the time going 50 km upstream compared to going 50 km downstream. The speed of the diver downstream is

• A. 3 km/h
• B. 6 km/h
• C. 4 km/h
• D. 5 km/h

Hint:

If the time taken upstream is $k$ times the time taken downstream over the same distance, then:
\[ \frac{u}{v} = \frac{k+1}{k-1} \]
Here, $k = 2$ and $u = 3$:
\[ \frac{3}{v} = \frac{2+1}{2-1} = 3 \implies v = 1\text{ km/h} \]
Downstream Speed = \( u + v = 3 + 1 = 4\text{ km/h} \).
This general formula is extremely useful for exams.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Downstream speed \( = \text{Still water speed} + \text{Current speed} \).
Upstream speed \( = \text{Still water speed} - \text{Current speed} \).
Time is inversely proportional to speed for a fixed distance.
Step 2: Key Formula or Approach:
1. Let speed of stream be \( v \).
2. Speed in still water \( u = 3 \).
3. Speed Downstream \( D = 3 + v \).
4. Speed Upstream \( U = 3 - v \).
Step 2: Detailed Explanation:
Time taken upstream is double the time taken downstream.
This means speed downstream is double the speed upstream.
\[ 3 + v = 2(3 - v) \]
\[ 3 + v = 6 - 2v \]
\[ 3v = 3 \implies v = 1 \text{ km/h.} \]
Downstream speed \( = 3 + 1 = 4 \text{ km/h.} \]
Step 3: Final Answer:
The downstream speed is 4 km/h.
This matches Option (C).