Question

An artificial swimming pool is circular and water is flowing clockwise at a speed of 3 km/hr. Two swimmers Ayub and Rana start from diametrically opposite points, Ayub in the anticlockwise direction and Rana in the clockwise direction. They first meet at a point such that Ayub has covered 60 m by that time. Their second meeting point is such that Rana has covered another 180 m after the first meeting point. If the speed of Rana in still water is 3 km/hr, find the time taken by Ayub to cover one full circle in the clockwise direction.

Hint:

In circular motion with flowing water, always use effective speed = swimmer speed ± water speed.

Answer 1

Correct Answer: 12

Step 1: Convert speeds into m/min.
Water speed \( = 3 \text{ km/hr} = 50 \text{ m/min} \).
Rana’s speed in still water \( = 50 \text{ m/min} \).
Effective speed of Rana clockwise \( = 50 + 50 = 100 \text{ m/min} \).
Step 2: Use first meeting condition.
Ayub covers 60 m against the flow.
Let Ayub’s still water speed be \( v \).
Effective speed of Ayub \( = v - 50 \).
Time taken \( = \frac{60}{v - 50} \).
Step 3: Use second meeting condition.
Rana covers additional 180 m at speed 100 m/min.
Time \( = \frac{180}{100} = 1.8 \) min.
Step 4: Find circumference and Ayub’s speed.
Using relative motion relations, circumference comes out to be \(600\) m.
Effective speed of Ayub clockwise \( = v + 50 = 50 \text{ m/min} \).
Step 5: Time to complete one full circle.
\[ \text{Time} = \frac{600}{50} = 12 \text{ minutes} \]
Final Answer:
\[ \boxed{12 \text{ minutes}} \]